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ON SENSATIONS FROM PRESSURE AND IMPACT 



WITH SPECIAL REFERENCE TO THE INTENSITY 
AREA AND TIME OF STIMULATION 



BY 

HAROLD GBIFFrSTG, A.B. 



SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 

IN THE 

University Faculty of Philosophy 
Columbia College 






NEW YORK 

1895 



ON SENSATIONS FROM PRESSURE AND IMPACT 



WITH SPECIAL REFERENCE TO THE INTENSITY 
AREA AND TIME OF STIMULATION 



BY 

HAROLD GRIFFIKGL A.B. 



SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 

IN THE 

University Faculty of Philosophy 
Columbia College 



NEW YORK 
1895 



v at 



CONTENTS. 



Introduction, 



PAGE 

i 



Sec. I 

Sec. 2 

Sec. 3 

Sec. 4 

Sec. 5 



CHAPTER I. 

The Quality of the Stimulus. 

Semi-organic Sensations and their Stimuli . . - 

Sensations of Touch and Temperature 

Active Touch . 

Passive Touch 

The Classification of Dermal Sensations 



Sec. 


i. 


Sec. 


2. 


Sec. 


3- 


Sec. 


4- 


Sec. 


5- 


Sec. 


6. 


Sec. 


7- 



CHAPTER II. 

The Intensity of the Stimulus. 

The Concept Intensity io 

Touch and Pressure n 

The Threshold for Pain - 14 

The Range of Pressure Sensations 16 

The Intensity of Sensation and the Intensity of the Stimulus ... 20 

Plaptic Sensations and Dermal Pain 24 

The Quality and Intensity of Sensation 27 



CHAPTER III. 

The Discrimination of Weights without Effort and the Intensity of 

the Stimulus. 



Sec. 1 

Sec. 2 

Sec. 3 

Sec. 4 

Sec. 5 



Preceding Investigations 

Further Experiments : Method of Procedure 

Results 

The Constant Error . 

The Confidence of the Observer 



29 

31 
38 
43 
44 



IV CONTENTS. 

CHAPTER IV. 
The Place of Stimulation. 

Page. 

Sec. i. Previous Investigations . 47 

Sec. 2. Further Experiments : the Accuracy of Discrimination 50 

Sec. 3. The Intensity of the Sensation 51 

Sec. 4. The Threshold for Pain 52 

CHAPTER V. 

Sensations of Impact. 

Sec. 1. The Threshold for Touch 54 

Sec. 2. The Threshold for Pain 55 

Sec. 3. The Analysis of Mass and Velocity in Impact Stimuli 57 

Sec. 4. The Discrimination of Mass and Velocity 59 

CHAPTER VI. 

The Area of Stimulation. 

Sec. 1. The Area of Stimulation and Judgments of the Intensity of the 

Stimulus 65 

Sec. 2. The Threshold for Touch 68 

Sec. 3. The Threshold for Pain 69 

Sec. 4. Theoretic Interpretation of Experiments on the Intensive Effect of 

the Area 71 

Sec. 5. The Area and the Discrimination of Intensity 73 

Sec. 6. The Intensity of Stimulation and the Discrimination of Areas . . 74 

CHAPTER VII. 

The Time of Stimulation. 

Sec. 1. The Intensity of Haptic Sensations in Relation to the Time : Low- 
Intensities 77 

Sec. 2. High Intensities 80 

Summary 84 



INTRODUCTION. 

The extent to which mental phenomena can be measured 
is not the least important of the many problems before 
Experimental Psychology. If one mental process is func- 
tionally related to another, it is possible for Psychology to 
become an exact science. If, however, the only measurable 
attribute of Mind is Time, Psychology can never hope to 
attain to the exactness of the physical sciences. 

The solution of this problem will be found only by expe- 
rience. The psychologist should not, moreover, be dis- 
couraged because Herbart's heroic attempt to apply to Psy- 
chology the methods of Mechanics was an ultimate failure, 
nor yet because Fechner's famous logarithmic law is not 
now generally accepted. Even if the measurement of men- 
tal relations be yet an open question, exact methods may be 
applied to the investigation of the subjective correlatives of 
measurable physical phenomena. The most obvious prob- 
lem of the kind is the relation between the intensity of 
stimulation and the corresponding sensation. But stimuli 
may vary in the time and area of application as well as in 
the intensity. If intensity be a measurable attribute of sen- 
sation, and if the time and area of stimulation be also related 
to the intensity of sensation, the relation of the four quan- 
tities may be expressed in the form of an equation : 

S=f(i, a, t). 

Only when such an equation is determined will the foun- 
dation be laid for the mathematical investigation of mental 
phenomena. For it is doubtful if exact methods can be 
applied to the study of mental relations, independent of 
physical phenomena, until the much simpler problems of 
Psycho-physics have been solved. 



2 SENSA TIONS FROM PRESSURE AND IMPACT. 

In the following pages we will discuss systematically the 
relations existing between the intensity, area and time of 
dermal stimuli, and the resultant sensations and perceptions. 
We will first, however, treat of dermal sensations with refer- 
ence to the quality of the stimulus. In this way we shall 
be in a position to appreciate more fully the significance of 
the effects of variations of the stimulus in quantity. 



CHAPTER I. 

Dermal Sensations and the Quality of the Stimulus. 

Sec. i. Semi-Organic Sensations and their Stimuli. 

Unlike the end-organs of the other senses, that of touch 
shows traces of the primitive sensibility of the entire peri- 
phery. Instead of being specialized in structure and func- 
tion, the skin has many different and independent functions. 
Even its sensory functions are quite distinct. Not only are 
tactile and temperature sensations utterly disparate, but 
equally distinct are many obscure sensations which, though 
apparently of dermal origin, seem allied in their vagueness 
and diffusiveness rather to the group of general or organic 
sensations. These may be called semi-organic sensations, 
since they represent the transition stage from those sensa- 
tions which refer to the outer world and those which refer 
only to the activities of the organism. Nevertheless, we 
are not justified in considering all dermal sensations as mem- 
bers of the organic group, as has been attempted by some. 
For temperature and pressure sensations are clearly the 
data for cognitions of the environment and not of the activi- 
ties of the organism. 

In the case of many of these sensations the stimuli are 
clearly some peripheral or other physiological processes in- 
dependent of external agency. Where the sensation appears 
to be induced by external stimulus, physiologists have en- 
deavored to explain the quality of the sensation by interme- 
diate processes which are considered the true stimuli in 
such sensations. Among such processes are irradiation, 
summation, vaso-motor disturbances, and sympathetic ner- 
vous action. The resultant Mitempfindungen are considered 
as the subjective effects of heterogeneous sensory excita- 

3 



4 SENSA TIONS FROM PRESSURE AND IMPACT. 

tions. 1 In the case of the tickle sensation, however, which is 
induced only by external pressure, such pressure must be 
considered as the stimulus, since it is the physical ante- 
cedent of a sensation. The intermediate neural processes 
may not, moreover, contribute so much to the quality of the 
sensation as may functional peculiarities of sensory cells. 
According to Bronson, indeed, the tickle sensation is a relic 
of a primitive contact sense which existed long before touch 
proper, and which is, therefore, closely related to the activi- 
ties of self-preservation and reproduction. 2 

Another state of consciousness, frequently of dermal ori- 
gin, is pain. If pain be a sensation, it must belong to the 
organic or semi-organic group ; and, in fact, is so classified 
by Weber, Funke, Wundt and others. 3 As it is not claimed 
that dermal pain is caused only by secondary nervous exci- 
tations, its relation to the stimulus will be discussed in an- 
other chapter. 

Sec. 2. Sensations of Touch and Temperature. 

In spite of the universal agreement that the tactile and 
temperature senses are utterly disparate, it has been claimed 
on experimental grounds that sensations of touch and temper- 
ature are causally related. Weber found that a cold coin was 
judged heavier than a warm one; 4 and Szabadfoldi found, 
conversely, that a hot wooden cylinder seemed heavier than 
one of the temperature of the skin. 5 Szabadfoldi experi- 
mented only on himself; but Weber's experiments were 
conclusive, and have been corroborated by Dessoir. 6 This 
writer questions Szabadfoldi's results, but we have con- 
firmed them in the following manner: 

1 Quincke, Zeit. fiir Klin. Med., Bd. xvii. 1890, 429; Goldscheider, Berlin. 
Physiol. Gesell., 1 890-91, no. I, 5 ; Kiilpe, Grundriss der Psy., 92 ; Wundt, Grund- 
ziige der Phys. Psy., iv. te Auf., 1, 408 ; Dessoir, Archiv. fiir Anat. und Physiol., 
1892, 324. 

2 Bronson, The Medical Record, xxviii. 425. 

'Weber, Wagner's Handbuch der Physiol., iii. 2 te Abth. ; Funke, Hermanns 
Physiologie, iii. 292 ; Wundt, op. cit., i. 544. 
4 Weber, op. cit., 512. 

6 Szabadfoldi, Moleschotf s Untersuchungen, IX, 624. 
* Dessoir, op. cit., 305. 



DERMAL SENSATIONS— QUALITIES OF THE STIMULUS. $ 

A 2 5 -cent silver coin was heated in water to a tempera- 
ture of from 50 to 55 C, and then placed carefully upon 
the palm of the observer's hand, the eyes being closed. It 
was then removed, and a similar coin heated to about the 
temperature of the skin was placed upon the hand. This 
was repeated a number of times, though occasionally the hot 
stimulus was the second to be applied. Four observers 
judged the hot coin heavier, and one showed no marked 
constant tendency. With one observer the writer applied 
two coins simultaneously, one over the other, the pressure 
of the two being compared with that of the hot coin. The 
one hot coin was judged heavier five times in ten trials, 
some of the observer's answers being guesses. From these 
experiments we conclude that pressure stimuli of low inten- 
sity and high temperature are judged heavier than those 
having the temperature of the skin. 

It does not follow, however, that all stimuli thus differing 
in temperature will give rise to such illusions. In order to 
ascertain whether hot or cold weights of high intensity are 
judged heavier, the writer applied to the palm of the hand 
a brass kilogram weight heated to about 50 C. This was 
removed and placed again upon the hand, but not in contact, 
a circular card-board of the area of the base lying between 
the weight and the skin. The hand of the observer was 
comfortably supported. Different persons served as sub- 
jects, and all were ignorant of the purpose of the experiment. 
As in the preceding experiment, a number of trials were 
made for each observer. Similar experiments were made 
with a cold weight and one which had no appreciable tem- 
perature effect on the skin. The cold weight generally had 
a temperature equal to that of the room, about 20 C, and 
at times much below this, so that from the area of stimula- 
tion, 16 sq. cm., and the conductivity of the metal, a marked 
sensation of cold was produced. It was found, as shown in 
the table of results given below, that stimuli of very high or 
low temperature are not judged heavier at 1000 g. In fact, 
the hot weight is rather judged lighter. In the table here 
given the figures denote the number of times the cold and 



6 SENS A TIONS FROM PRESSURE AND IMPACT. 

hot weights were judged heavier or lighter than those of 
moderate temperature. 



j 


Cold weight, i kg 


Hot weight, i kg 


Observer. 


Heavier. 


Lighter. 


Heavier. 


Lighter. 


L. F. 
S. F. 
K. 

M. G. 
J. G. 


2 

2 
7 

5 


6 

3 
3 

5 


2 

o 

2 

4 
4 


8 

IO 

5 
6 

6 


Total, 


16 


17 


12 


35 



The results above given go to show that tactile and tem- 
perature sensations are not related, as Weber 1 and Szabad- 
foldi 2 inferred. Dessoir's explanation is that the illusion is 
due to the contraction of the skin from the lower tempera- 
ture, and consequent increase in the number of sensory- 
nerves that are affected. 3 But heated coins are overesti- 
mated, and according to this hypothesis they should be 
underestimated. A more satisfactory explanation is that an 
illusion of judgment is involved. 4 This is rendered plausible 
by the fact that stimuli of high intensities are not over- 
estimated. We may suppose that the mind tends to infer 
from the intensity of the temperature sensation that the 
corresponding stimulus is of greater magnitude, and there- 
fore heavier than the stimulus causing a purely haptic 5 
sensation of but little intensity. For heavy weights we 
should on this hypothesis expect underestimation rather than 
overestimation, of hot or cold stimuli, and that there is some 
such tendency, at least for hot weights, the experiments 
seem to show. The objection of Dessoir against such an 
explanation is, we think, inconclusive. A difference in dis- 

1 Weber, op. cit., 551. 

2 Szabadfoldi, op. cit. 

3 Dessoir, op. cit., 306. 

4 Cf. Funke, op. cit., 321. 

5 We use the term haptic (Greek dirTdofiai) of all sensations of contact, touch, 
pressure or impact. For this term we are indebted to Dessoir. 



DERMAL SENSATIONS— QUALITIES OF THE STIMULUS. 7 

crimination-time for weight and temperature when only the 
quantity judged is variable, does not preclude such an illu- 
sion when the conditions are different. 

The other experimental evidence in favor of any funda- 
mental relation between haptic and temperature sensations 
is equally inconclusive. The fact that heavy weights seem 
hotter or colder than lighter weights, as stated by Noth- 
nagel, 1 may be due to differences in conduction arising from 
differences in contact. Wunderli found that observers had 
difficulty in distinguishing tactile from temperature stimuli 
of low intensity. 2 But the errors occurred only when the 
back was the surface stimulated, and though temperature 
stimuli were confused with tactile stimuli, the reverse error 
did not occur. As we are not accustomed to temperature 
sensations in the back, such a confusion is but natural, espe- 
cially when the stimuli are of such low intensity that the 
process of perception is obscured. 

Sec. 3. Active Touch. 

The great majority of so-called tactile sensations are in 
reality results of complex kinaesthetic and haptic sensory 
elements. In fact, many have distinguished between active 
and passive touch. Dessoir opposes contact sensations to 
those of pselaphesia, 3 and Bronson goes so far as to consider 
contact sensations and those of active touch not only as quite 
distinct but as having different end organs. 4 It is clear, 
however, that active touch may involve movement with or 
without muscular effort, or, conversely, muscular effort with 
or without movement. We have, therefore, a triple set of 
sensory impulses to consider as the physiological antecedents 
of the sensation of active touch. 

Many psychologists have explained the sensation of move- 
ment by alterations in the tension of the skin and by atmos- 
pheric pressure. 5 This view is apparently corroborated 

1 Nothnagel, Deutsches Archiv. fiir Klin. Med., II, 298. 
3 Wunderli, Moleschott 's Untersuchungen, VII, 393. 
'Dessoir, op. cit., 242. 
4 Bronson, op. cit. 

5 For references see the works of Wundt and James, and Delabarre, Ueber Be- 
wegungsempjindungen, Freiburg, 1891. 



8 SENSA TIONS FROM PRESSURE AND IMPACT. 

by the influence of dermal anaesthesia or hyperaesthesia 
on the perception of movement. The pathological evidence 
proves that dermal sensations enter into those of movement, 
but that is all. Other well authenticated observations show 
that anaesthesia does not necessarily affect the perception of 
movement. In complexes of tactile and kinaesthetic sensa- 
tions we must, therefore, assume different sensory processes. 
But active touch is possible without movement either of 
the stimulus or the sense organ. If through an act of 
volition we exert pressure upon an external object, we have 
in addition to the sensation of dermal pressure that of effort. 
In fact, all the feelings of strain and tension are felt which 
enter into the muscular consciousness. As pathological ob- 
servations and experiments on lifted weights prove the 
muscular sense to be independent of touch, 1 it is evident that 
where pressure is exerted voluntarily the resultant sensation 
is complex, and not a haptic sensation proper. We have, 
therefore, to distinguish between what we might call subjec- 
tive pressure, or pressure with effort, and objective pressure, 
or pressure without effort. 

Sec. 4. Passive Touch. 

Having analysed the various elements entering into tactile 
complexes, we turn to those sensations in which the subject 
is passive and the stimulus acts only upon a definite area. 
The stimulus may then be pressure exerted upon the skin, 
the energy of a body striking the skin, or traction tending 
to separate the dermal end organ from the organism to which 
it belongs. These stimuli are qualitatively different, as are 
the corresponding sensations, though for traction these are 
less distinct than would be supposed. 2 The blow of a mov- 
ing object upon the periphery gives rise to a sensation dis- 
tinct from that of a motionless weight. This difference 
increases with the velocity of the moving mass. The stim- 
ulus in such sensations, therefore, is to be considered the 
product of the mass and its velocity, or some function of its 
velocity. The resulting sensation may be called a sensation 
of impact, as distinguished from one of pressure. 

1 See Wundt, op. cit., 427; Delabarre, op. cit., 37, 38. 
"See Hall and Motora, Am. Journal of Psy., I, 72. 



DERMAL SENSATIONS— QUALITIES OF THE STIMULUS. O, 

But is not this difference between pressure and impact 
only a difference in degree? When a weight is applied to 
the hand there must be some impact, whatever be the veloc- 
ity at which the weight be applied. If a weight of low 
intensity, as ioog or less, be applied, and the area of stimu- 
lation be not too small, the sensation is one of impact ; but if 
a stimulus of moderate intensity be used, a distinct pressure 
sensation will be observed in addition to that of impact. 
This is due to the effect of the weight in overcoming the 
elasticity of the skin and depressing the dermal tissues. The 
stimulus in pressure sensations may, therefore, be considered 
not momentum or kinetic energy, but rather as mechanicaL 
force exerted through the object in contact with the skin, or 
more accurately, the work done by this force in displacing 
the dermal tissues. In reality, however, the process of 
stimulation is often more complex. When the pressure is 
sufficiently great to produce motion, kinaesthetic elements 
will affect the sensory result. When movement is prevented 
by opposing forces, a double process of dermal stimulation 
will result, since action and reaction are equal and opposite. 

Sec. 5. The Classification of Dermal Sensations. 

The general results of the analysis above given may be 
summarized in a classification of dermal sensations with 
special reference to the quality of the stimulus : 



Dermal 
Sensations 



Simple, or 
Purely Dermal 



Compound, 
or 
Semi-Dermal 



( Traction. 
Haptic i Objective pressure. 
( Impact. 

( Heat. 



Temperature 



Semi-organic 



Subjective 
Pressure 



Kinaesthetic 



Cold. 
Tickle. 
Itching. 
Creeping. 
Pain. 
fWith 
movement. 
Without 
movement. 
With effort. 
Without 
effort. 



CHAPTER II. 

The Intensity of Stimulation. 

Sec. i. The Concept Intensity. 

The term intensity, as applied to neural stimuli, has long 
been in universal use among psychologists, but frequently in 
.a manner that is far from exact. In physical science the 
term is used as the quantitative predicate of force. But 
many stimuli, as those of smell and taste, cannot be meas- 
ured in terms of force. To avoid ambiguity in the use of 
this term, we would suggest as a working definition of in- 
tensity, as used in Psychology, the following, which is based 
upon obvious psychological grounds : that quantitative prop- 
erty of neural stimuli, the magnitude of which determines 
whether or not they give rise to a sensation ; and, if so, 
whether that sensation be painful, or have only the particu- 
lar quality due to the quality of the stimulus. 

From this point of view the intensity of visual and audi- 
tory stimuli may be measured by the energy of motion 
transmitted to the end organ in a given time. The inten- 
sity of gustatory and olfactory stimuli may be measured for 
a given substance by the quantity which is applied to the 
end organ. But with temperature stimuli the measure of 
intensity is more complex. Then, too, as heat and cold are 
physically the same, the absolute measure of heat is not the 
measure of the intensity of heat, as regards its physiological 
and psychological effects. Passing from the temperature 
sense to that of effort, the work done by muscular contrac- 
tion in a given time is clearly the measure of intensity ; but 
when no motion takes place the criterion is different, as 
such units cannot be used. In this case the measure of in- 
tensity is clearly the force which is exerted. 

The measurement of the intensity of haptic stimuli is, 
fortunately for our purpose, comparatively simple. When 
10 



THE INTENSITY OF STIMULA TION. 1 1 

impact may be neglected, the intensity of the stimulus is 
measured by the weight that is applied ; for the work done 
in depressing and displacing the dermal tissues will be pro- 
portionate to the impressed force. When, however, appre- 
ciable movement occurs before the full pressure is exerted, 
the matter is more complex, since the subjective effect is 
dependent not only on the mass but also on its velocity. 
We might suppose that the measure of the intensity of an 
impact stimulus would be the product of the mass and the 
square of the velocity, since this quantity represents the 
energy of the blow. But, as we shall find in the chapter on 
Sensations of Impact, the square of the velocity does not 
appear to have as intensive an effect as does the mass. 

Sec. 2. Touch and Pressure. 

It was shown by Aubert and Kammler that pressure and 
impact stimuli, below a certain intensity, are not perceived. 1 
The sensations from stimuli of low intensity are sensations 
of passive touch, the element of pressure being apparently 
absent. From such data Meissner inferred that pressure 
sensations are absolutely distinct from those of touch proper, 
einfache Tas temp find ungen, and that these have special end 
organs, the tactile corpuscles. 2 Meissner's distinction be- 
tween touch and pressure is accepted by Aubert and Kamm- 
ler, Bronson and Dessoir, but is rejected by Funke, Wundt 
and Kiilpe. We shall now consider in detail the evidence 
that has been brought forward to support this view. 

According to Meissner, touch furnishes the data for the 
concept of externality, and accompanies all pressure sensa- 
tions, though not necessarily accompanied by them. 3 Clearly, 
however, this is but an hypothesis to account for what is 
assumed, that is, the difference between touch and pressure. 
Aubert and Kammler reject Meissner's hypothesis, basing 
their distinction upon their alleged observation that contact 
sensations are subjective modalities. This does not accord 

1 Aubert and Kammler, Moleschoti 's Untersuchungen, v. 145. 

2 Meissner, Zeitschrift fur Rat. Med., 2 te R., iv. ; also, Beitrage zur Anatomie 
und Physiol, der Haut, Leipzig, 1853. 

'Meissner, op. cit., 272. 



12 SEJVSA TIONS FROM PRESSURE AND IMPACT. 

with the introspection of the writer. The apparent differ- 
ence observed may be due to the fact that stimuli of low 
intensity do not give rise to sensations of sufficient clearness 
for the mind to perceive the quality of the stimulus. We 
certainly do refer a tactile sensation to an external something y 
though what that may be we may not know. 

Dessoir gives as the characteristic of pressure sensations 
the feeling of effort which is involved. 1 But Dessoir un- 
doubtedly refers to subjective pressure, or pressure with 
effort; and as sensations of pressure are possible without 
effort, the criterion is not applicable. 

Bronson bases his separation from pure contact of psela- 
phesia, or perceptive touch, partly upon the above facts of 
introspection and partly upon the apparent relationship of 
sensations of contact to semi-organic sensations. 2 Accord- 
ing to Bronson, sensations of contact require as their peri- 
pheral antecedents only the stimulation of the epidermal 
fibrillar, and are, therefore, to be considered distinct and 
primitive sensations. 

However conclusive be Bronson's arguments as to the 
biological theory of dermal sensations, they do not prove 
touch to be distinct from pressure, because the tickle sensa- 
tion does not necessarily accompany that of contact. It is 
a distinct state of consciousness independent of the tactile 
sensation, and the same may be said of the aphrodisiac sense. 
We conclude, therefore, that there is no psychological basis 
for the distinction, unless there be other evidence than that 
which we have discussed. If touch and pressure were dis- 
tinct, we should look for such evidence in pathology ; but 
the writer knows of none. Bronson states that hyperaes- 
thesia and apselaphesia may coexist. But it is probable that 
he really refers to hyperalgesia, which is quite irrelevant. 
According to Richet, tactile hyperaesthesia is unknown. 3 
There have been instances of anaesthesia for pressure stimuli 
of low intensity without anaesthesia for those of high inten- 

1 Dessoir, op. cit. , 242. 

' Bronson, op. cit. Bronson does not state these arguments categorically, but the 
above appears to be his position. 

'Richet, Re'cherches sur la Sensibilite, 219. 



THE INTENSITY OF STIMULA TION. 1 3 

sity. 1 But, as Richet observes, this may be explained by 
the fact that the nerves die first at their extremities. 

Apart, however, from these negative considerations, it 
must be admitted that the classification of one group of sen- 
sations, as distinct from another group, logically implies our 
inability in introspection to pass gradually from one to the 
other. By this criterion the sense of touch and that of 
pressure must be identical. It is impossible to tell where 
one begins and the other ends. Stimuli that are barely per- 
ceptible may be judged with reference to their weight. 2 On 
the other hand, individuals differ as to what they call pres- 
sure. In the course of experiments on the threshold of 
pain, to be described in the next section, one observer said 
he began to feel pressure at 3.5k., pain appearing at 8.5k. 
The writer would call that sensation one of pressure when 
the instrument used registered only 1.0k. 

Even if touch and pressure be indistinguishable, the ap- 
parent change of quality requires an explanation. That 
generally given is that different physiological processes are 
induced by intense stimuli. Aubert and Kammler explain 
the distinction by the displacement of the skin. But this dis- 
placement varies with the intensity of the stimulus. 3 Kiilpe 
mentions the effect of intense pressure upon the muscular 
tissues, 4 but we have pressure sensations where there are no 
muscles. Meissner's hypothesis, to which that of Bronson 
is similar, that the sensory cells in the dermis are the ana- 
tomical basis of pressure sensations, is inadequate, since 
these cells appear to be absent on parts that are sensitive to 
pressure. 5 Goldscheider found special pressure spots, 6 but 
his results, both histological and psychological, are dis- 
puted. 7 The writer's own observation does not enable him 
to detect the existence of points that give pressure or con- 
tact sensations only. Certain spots may be more sensitive 

1 Richet, op. cit., 227. 

a See Chapter III., Section 3. 

• For measurements of this, see Hall and Motora, op. cit. 

* Kiilpe, op. cit., 91. 

6 Cf. Wundt, op. cit., i. 302 ; Dessoir, op. cit., 275. 

•Goldscheider, Archiv. fur Anat. und Physiol., 1885 Supp. Bd., 76. 

7 Cf. Dessoir, op. cit., 251. 



14 



SEA T SA TIONS FROM PRESSURE AND IMPACT. 



than others, but this would throw no light on the question. 
Besides, it is difficult to obtain a distinct sensation of pres- 
sure when so small an area is stimulated as is necessary in 
such experiments, since the sensation of pressure passes so 
quickly into that of pain or other semi-organic sensations. 

But if there is no additional process of sensory excita- 
tion in pressure sensations, in what way may the apparent 
difference be explained? Our answer is that there is no dif- 
ference in sensation, but only in perception. What we 
mean by a sensation of pressure is one of such a quality that 
we can ascribe the subjective effect to some definite objective 
cause and one exerting such pressure that its removal would 
involve appreciable muscular work. The apparent differ- 
ence may, we think, be thus explained, for it is impossible to 
analyse in consciousness the mental reaction in perception 
out ol the total sensational and perceptive complex. 

3. The Threshold of Pain, 

For the purpose of measuring the intensity of pressure 
causing pain a spring dynamometer was used by which 
a given pressure could be exerted upon any surface. 1 
Attached to the lower end of the spring 
was a sliding cylindrical piece of brass. 
This was capped with hard rubber (A), 
which was applied to the surface to be 
stimulated. The cap which came in con- 
tact with the skin was hemispherical, and 
about 8mm. in diameter. The pressure was 
exerted by the hand of the experimenter, 
and the amount of pressure was registered 
in kilograms by the movable piece (B) 
attached to the spring. The scale was 
tested by an accurate balance adapted to 
heavy weights, and was found to be free 
from appreciable error. The stimulus was 
applied by the writer to the volar surface 
of the left hand of the subject over the fifth meta- 

1 This instrument was devised by Prof. J. McK. Cattell. He has suggested the 
term algometer by which to designate it, and this expression will be used hereafter. 



Fig. 1. 




E 



A 



J 



THE INTENSITY OF STIMULATION. 



IS 



carpal. The pressure was increased as nearly as possible 
at the same rate for different observers, about 1.4k. per 
sec. If we take .3 sec. 1 as the double reaction-time, we 
have to subtract i.4X-3=.4k. from the reading of the instru- 
ment. The observers were asked to speak when the in- 
strument began to hurt at all or be uncomfortable ; for it was 
found that individuals differed as to what they called 'pain.' 
The subjects tested were students in Columbia and Barnard 
Colleges and in private schools. 2 Below we give the average 
in kilograms as well as the maxima and minima corrected for 
the constant error above referred to. The approximate ages 
are also given. 



Ob- 
servers. 


50 Boys. 


40 College 

Students. 

(Men.) 


38 Law 

Students. 


58 
Women. 


40 College 
Students. 
(Women.) 


Ages, 


12 to 15 


16 to 21 


19 to 25 


16 to 20 


17 to 22 


Av., 


4.8 


5-i 


7.8 


3-6 


3-6 


Max., 


8.4 


13.6 


i5 + 


7.6 


S.6 


Min., 


2.1 


1.9 


3-9 


1.8 


1-7 



From the above results it appears that although individu- 
als differ greatly in sensitiveness to pain, on the whole women 
and boys are more sensitive than men. The variations in 
those of the same age and sex are not due to chance, since 
any one person when tested gives fairly constant results. 
Nor are they due to individual differences in perception and 
judgment, though doubtless these affect the results to some 
extent ; for it is very easy to tell when the pressure begins 
to be uncomfortable, and the ' imagination ' does not seem 
to be a disturbing factor. Indeed, the pain seems often to 
come with greater suddenness. These variations are rather 
to be ascribed to constitutional nervous differences, and in 
part, perhaps, to differences in the thickness of the skin. 



1 This was verified by chronoscopic measurements. 

2 The writer takes pleasure in acknowledging his indebtedness to Registrar Mrs. 
N. F. Liggett and Principals Miss Brown and Mr. Cutler for furnishing him the 
opportunity of making the tests on young women and boys. 



1 6 SENS A TIONS FROM PRESSURE AND IMPACT. 

Sec 4. The Range of Pressure Sensations. 

If the minimum tangible, or tactile threshold (T), were 
measurable, as is the threshold of pain (P), and if the sensa- 
tion of pressure ceased as soon as that of pain appeared, we 
could determine the range of haptic sensations (R) by the 
formula: pi 

R = — 
T 

Since the haptic sensation does not cease when pain 
begins, but rather decreases gradually as the pain increases, 
the so-called range cannot be measured. We may, however, 
use the term to indicate the extent of haptic sensations up to 
the pain threshold. But are we justified in assuming the 
pain threshold to be a quantity ? According to the algedonic 2 
tone theory we are not so justified. And, even assuming 
that a stimulus becomes painful at a certain point, the one 
sensation is at first so obscured by the other that it is not im- 
mediately appreciable. Nevertheless, the appearance of 
pain is generally so sudden when the stimulus is increasing 
in intensity, that we treat the threshold of pain as approxi- 
mately a quantity. 

Assuming then that the range, and therefore the thres- 
holds of touch and pain, can be measured, it is evident that 
in determining them the conditions of stimulation should be 
constant. Not only the time and space conditions, but also 
the mode of applying the stimulus, must be constant. 

In the measurements of the tactile threshold made by 
Aubert and Kammler the element of impact was involved, and 
their results could not be compared with our own measure- 
ments of the pain threshold, since in these impact was ex- 
cluded. Bloch employed the same method, that of pure 
pressure, 3 but his experiments were made on himself, and 
we judge them, therefore, inconclusive. We found that re- 
sults are obtained under such circumstances quite different 
from those obtained when the stimulus is applied by another 

1 Cf. Wundt, op. cit., I, 335. 

2 We have borrowed this translation of Gefiihlston from Marshall, Pain, Pleasure 
and Aesthetics. 

3 Bloch, Archives de Physiologie, 1891, 322. 



THE INTENSITY OF STIMULATION. \J 

person and the observer is ignorant of the time of applica- 
tion. Bloch gives .ooo5g to .001 5g as the smallest appre- 
ciable pressure. Aubert and Kammler found for an area of 
9mm, .oo5gas the 'minimum tangibile. The results above given 
are much more discordant than they might at first seem, 
since the greater value for the threshold is obtained for the 
smaller area, 1 and since impact is clearly involved rather than 
pressure. 2 

In order to make further experiments on the smallest 
perceptible haptic stimuli, the writer constructed an instru- 
ment similar to that used by Bloch. 

Fig. 2. 




3B 



To a wooden handle (B) was attached by wax a horizontal 
bristle (AC), taken from an ordinary broom. At the end (A) 
was fastened by wax a vertical piece (AD) of the same 
material, the point of which was applied to the part stimu- 
lated. The pressure was exerted by the hand of the experi- 
menter. The degree of pressure was shown by the elevation 
of the bristle, which was read off on a scale (FK). The 
readings on this scale were in grams, the elevations corre- 
sponding to different pressures having been found by a bal- 
ance. The pressure was applied upon a circular card board 
about .9cm in area. This card was so light, .05g, that its 
weight could be neglected after the moment of application, 
as it rested on the skin during the experiments. The 
observer's eyes were closed, and he did not know when the 
stimulus was applied. The rate of application of the pres- 
sure was kept as constant as possible. It was as rapid as 
was consistent with taking the readings, about .3g per sec. 

1 See chapter V, sec. 2. 
1 See chapter VI, sec. 2. 



18 



SENSATIONS FROM PRESSURE AND IMPACT. 



We subtract, therefore .3X.3=.ig from the reading ob- 
tained. Ten experiments were made on S. F., and also on 
G., the writer, for the smallest perceptible pressure, T. 
The same number were made for the threshold of pain, P, 
by means of the dynamometer already described. The area 
of stimulation for the pain measurements was also .9cm. 
The results are given in grams. The values of the Range, 
R, are found by dividing the average values of P by the 
average values of T. 





Av. 


T. 
Max. 


Min. 


Av. 


P. 
Max. 


Min. 


P 

R = — 

T 


F. 
G. 


1.9 
2.6 


2.7 
2.5 


1. 

•4 


3230 
4400 


4300 
5700 


2700 
3800 


1700 
1697 



According to these results the haptic range is about 1700. 
The great variation in the values obtained for the thresh- 
old renders these figures necessarily very inexact. The 
values of the threshold here given are very much greater 
than those obtained by previous investigations. The elimi- 
nation of the element of impact 1 and of the knowledge of 
the observer would tend to give far greater values than those 
obtained by Bloch and by Aubert and Kammler. Then, too, 
the area and time of stimulation are factors not to be neg- 
lected ; but these differences are not such as to affect the 
results appreciably. 2 

It is generally assumed that the threshold is a definite 
quantity. 3 In the case of sensations of pain, the results 
obtained for any individual are sufficiently constant to justify 
this assumption as a working hypothesis. The results given 
above for the tactile threshold are, however, so variable 
that we are led to doubt the validity of such an assumption. 
In fact, the very conception of a threshold involves a logical 
contradiction. If by this we mean a quantity that we can 
always perceive under moderately constant conditions of 

1 See Chapter V, Sec. i. 

8 See Chapter VI, Sec. 2 ; Chapter VII, Sec. I. 

* Wundt, op. cit., I, 334; Ktilpe, op. cit., 51 ; Ladd, Elements of Phys. Psy., 363.. 



THE INTENSITY OF STIMULATION. 1 9 

attention, we shall have to assume a quantity much larger 
than what we often perceive. In the course of experiments 
on the perception of differences in weights, the application 
of a stimulus of 5g was unobserved several times, and that, 
too, by an excellent subject, who was expecting the stimulus 
at the time of application. 1 Even a stimulus of ioog has been 
unobserved by good observers in experiments by the method 
of right and wrong cases. We must conclude, then, that 
stimuli of a given intensity will be observed a certain pro- 
portion of times and no more, if a sufficient number of 
experiments be made. We may also infer that stimuli far 
below the so-called threshold will be observed, some times, 
at least, in an infinite number of trials. What, then, shall 
we call the threshold? It is not the quantity that is always 
observed, for this would involve a contradiction. It is not 
that which is observed a certain percentage of trials, for 
this could not be called the least perceptible intensity. We 
can only say that the probability that a given stimulus will 
be perceived by the observer is functionally related to the 
intensity of the stimulus. In fact, the so-called threshold 
is no more a definite quantity than the so-called least notice- 
able difference, which we think leads, when discussed from 
the standpoint of probabilities, to a similar reductio ad absur- 
dum? Indeed, the processes involved are much the same. 
Not the least important of the factors entering into the 
measurement of one as well as the other, is the confidence 
of the observer, which varies from extreme doubt to absolute 
certainty. 3 The wrong cases, or mistakes due to errors of 
observation, which occur when different stimuli are com- 
pared, have their counterpart in tactile hallucinations, a 
number of which occurred in the course of our experiments 
on the threshold. 4 

1 See Chapter III, Sees. 2 and 3. 

2 Fullerton and Cattell, On the Perception of Small Differences, 10 ; Pierce and 
Jastrow, National Academy of Sciences, 1884, III, 75. 

3 See Chapter III, Sec. 5. 

* Cf Krohn, Journal of Mental and Nervous Diseases, March, 1893, 14. 



20 SENS A TIONS FROM PRESSURE AND IMPACT. 

Sec. 5. The Intensity of Sensation and the Intensity of the 
Stimulus. 

This relation has generally been investigated by deduc- 
tions from the relation of the least noticeable differences to 
the absolute intensity of the stimulus. But, as is shown by 
the application of the method of right and wrong cases, there 
is no such quantity, and therefore the deductions based upon 
it are invalid. Of the other psycho-physical methods, two 
have been applied by Merkel to the investigation of haptic 
sensations. 1 By the method of double stimuli it was found 
that the ratio of the normal to the estimated double stimu- 
lus was approximately 1 : 2 for from ioog to 2000g. By the 
method of mean gradation Merkel found that the values of 
the estimated arithmetic mean of two stimuli was but slightly 
less than the true arithmetic mean. Merkel's experiments 
were, however, made only on himself, and the muscular 
sense was not excluded, so that his results are not con- 
clusive. 

In the hope of throwing some light on the much dis- 
cussed psycho-physical problem in pressure sensations, ex- 
periments were made by a method different from those gen- 
erally used, the observer being required to judge of two 
stimuli how much greater one was than the other. The 
method of experiment in detail was as follows. A wax 
mould having been constructed to fit the left hand, the hand 
was placed in this, the palm being upward under the pan of 
a balance. The pressure was given by weights placed upon 
the pan of the balance. The pressure was transmitted to 
the hand by means of a piece of wood glued to the pan. A 
circular cap of cardboard attached to the end of the stick, 
and about 4 mm in diameter, came in contact with the skin. 
The observer having closed his eyes, and the cardboard cap 
being barely in contact with the skin, a weight was care- 
fully placed in the pan, and after about two seconds was 
removed and replaced by a weight very much heavier, the 
observer being asked to judge the ratio of the weights. But 
few experiments were made at one sitting, so that memory 

1 Merkel, Philosophise he Studien, v. 253. 



THE INTENSITY OF STIMULATION. 



21 



could not affect the results. For purposes of convenience 
the lowest stimulus was applied first, the next higher follow- 
ing ; but the reverse order was at times adopted without per- 
ceptible difference. The observers were, of course, ignor- 
ant of the objective relations of the weights as well as of 
the purpose of the experiment. They were all students of 
Psychology. In the table appended are given the results. 
The first horizontal column denotes the stimuli in grams. 
The numbers in the vertical columns, under those denoting 
the stimuli, indicate the average judgments as to how many 
times the given stimulus was greater than the stimulus pre- 
ceding. Thus S. F. judged 50 g., 3.1 times as heavy as 10 g, 
and 2 50g., 4.2 times as heavy as 50 g. The figures preceded by 
the sign zb denote the probable error of the given average. 1 
But few experiments were made on each observer, for 
not only were the mean variations small, but the individual 
differences were very great. 



Observer. 


No. expts. 


2g. 


IOg. 


50 g. 


250 g. 


1250 g. 


1800 g. 


S. F. 


10X4 


— 


— 


3-i±-Oi 


4.2±.03 


7.i=b.o4 


3.8±.04 


L. F. 


6X4 


— 


— 


2.0db.00 


2.7±.oo 


4.9+. 01 


3.Q l ±-oi 


P. 


5X5 


— 


2.2zb.OO 


2.5±.OI 


3.o±.oo 


5-6±.03 


3-4^.01 


K. 


5X5 


— 


I.9=h.OO 


i.gzb.oo 


2.I±.00 


3.4=*=. 00 


I.7dr.OO 


Av. 


— 


— 


2.0 


2.4 


3.0 


5-2 


3.0 s 



In order to represent the relation between the stimulus 
and the estimate of the stimulus, let us take the number 2 as 
representing the estimated weight at 2 g. Multiplying this 
by the estimated values of 10 g. in terms of 2 g., the number 
obtained will represent the increase of the estimate of the 
stimulus as the stimulus increases from 2 to 10. In like 
manner, by taking this result and multiplying it by the esti- 

1 This is such an error (or deviation from the average) that half of the errors 
would be smaller and half would be larger. It is here obtained by the briefer formula, 

p^ .845 Sv 



n y/n — 1 
See Merriman, Airy and other writers on the theory of probabilities and the method of 
least squares. 

* This number refers to 2500 g., not to 1800 g., as do the others in this column. 

• This average is based upon 3 values, 3.8, 3.4 and 1.7. See note 1. 



11 



SENSATIONS FROM PRESSURE AND IMPACT. 



mated values of 50 g. in terms of 10 g., we obtain the in- 
crease of the estimate as the stimulus increases from 10 g. 
to 50 g. In the case of S. F. and L. F., as no measurements 
were made of the estimate of 10 g. in terms of 2 g., we take 
as the unit of estimated weight at 10 g. 4.4, which is the 
value obtained for P., with whose results those of S. F. and 
L. F. fairly agree. 1 In this way the relative increase of 
the estimate of weights is obtained. The increase of the 
stimulus is shown by the intensities used, these being, with 
the exception of the highest, in geometrical progression. 
Below are given the calculated values of the estimates of the 
stimuli : 



Observer. 


2 g- 


iog. 


5og. 


250g. 


I250g. 


i8oog. 


S. F. 


— 


4 .4 2 


13. 


57. 


404. 


1535. 


L. F. 


— 


4-4 3 


9- 


23- 


I 12. 


433- 4 


P. 


2 


4.4 


11. 


33. 


185. 


629. 


K. 


2 


3-8 


7.2 


15. 


51. 


86. 


Av. estimate of 














stimulus, 


2 


4.2 


10. 


32. 


188. 


750. 4 



The relations here expressed are graphically represented 
in the accompanying curves. The ordinates express the 
estimates of the intensity of the stimulus, and the abscissae 
the true intensities in grams. 

In interpreting these results we may assume that the 
intensity of sensation increases in proportion to the esti- 
mated increase of the stimulus. Such an assumption would 
be illegitimate, if the stimuli were such that the observers 
could judge them by some means other than their effect on 
sensation. But where the muscular sense is excluded, as in 
these experiments, association cannot very well influence the 

1 2 g. was found to be so often inappreciable by S. F. that the determination based 
upon it was difficult. The experiments on L. F. were made before it was decided 
what weights had best be used. 

1 These are taken as units, as explained above. 

8 This number refers to 2500 g. instead of 1800 g. 

4 Based upon three values. See note 3. 



THE INTENSITY OF STIMULATION. 



23 



results ; for the concept of weight is based upon sensations 
of effort. Assuming, then, that a relation is obtained be- 
tween the intensity of the stimulus and that of the sensation, 

Fig. 3. 




150 



115-0 



lioo intensity 



It is evident that for moderate intensities the sensation 
increases much more slowly than in direct proportion to the 
stimulus. As the stimulus approaches the pain threshold, 
the sensation appears to increase at a much greater rate than 
before. The individual variations are so great as to render 
impossible an analytical expression of the relation. Never- 
theless, the shapes of the different curves are similar. It is 
clear, moreover, that a logarithmic relation as demanded by 
Fechner's law does not hold, even within narrow limits, for 
any one of the observers. If such were the case, the esti- 
mates of the stimulus would increase arithmetically, since 
the stimulus increases geometrically. 

It is, however, possible that this relatively rapid increase 
for high intensities is due to processes of perception and 
judgment, and not to real differences in the rate of increase 
of the sensation. As stimuli approach the pain threshold, 
the consciousness of impending pain may cause us to over- 
estimate the magnitude of the stimulus. This might happen 
in either of two ways. In the first place, since the sensation 
of pain and that of pressure are heterogeneous, we might 
suppose that the mind would unconsciously assume great 



24 SENSA TIOJVS FROM PRESSURE AND IMPACT. 

objective differences in quantity as causally related to sub- 
jective differences in quality. Another possible explanation 
is that the sensation of pain, tending to occupy the field of 
consciousness to the exclusion of other presentations, is to 
be considered as essentially a sensation of great intensity ; 
from which it follows that stimuli causing pain, or approach- 
ing the pain threshold, are estimated as relatively of greater 
intensity than those into the perception of which the element 
of pain does not enter. 

Sec. 6. Haptic Sensations and Dermal Pain. 

We have already found, in Chapter I, that the peculiar 
quality of the tickle sensation is not logically ascribable to 
the quality of the stimulus. We may state, therefore, that 
sensations differing in quality may be caused by stimuli differ- 
ing in quantity. It is not, however, near the lower limit of 
haptic stimulation that this qualitative transition is most 
marked. If pain be considered a sensation, two disparate 
sensations are induced by high as well as low intensities of 
dermal stimuli. If, however, pain be considered but an 
intensive form of an element existing in all sensational states 
of consciousness, such a generalization is impossible. 

According to the commonly accepted view, the algedonic 1 
tone of a sensation is negative, that is, unpleasant, for very 
low intensities, but upon increase in the stimulus becomes 
positive. As the stimulus is further increased, a maximum 
of the positive values is reached, after which the algedonic 
tone rapidly decreases. This doctrine has, undoubtedly, 
many theoretic advantages. But it does not seem to accord 
with the observed phenomena of dermal sensation. In the 
experiments on pain already described, the appearance of 
pain was generally quite sudden. If the pain consciousness 
were merely an intensive form of what accompanies all 
dermal stimulation, we should not expect such sudden trans- 
itions. Then, too, in the writer's experience, at least, there 
is no pleasurable element whatsoever in a haptic sensation 
of moderate intensity. It may be said that we prefer certain 

1 Wundt, op. cit. I, 558 ; Kiilpe, Grundriss der Psychologies 256. See also the 
writings of Ward, Sully, and Bain. 



THE INTENSITY OF STIMULATION. 2$ 

intensities to others. But this is not necessarily due to dif- 
ferences in their algedonic tone. The very fact that one 
stimulus may be preferred to another when there is no con- 
scious pleasure or pain, tends to show that the phenomenon 
is due to complex processes of association. 1 The pressure 
acting- on a small area will, on this hypothesis, be judged 
unpleasant because we tend to think of the pain that would 
result if the area were much diminished, or the intensity of 
the stimulus much increased. In like manner, a stimulus of 
moderate intensity is preferable to one of very low intensity, 
because for low intensities perception is less distinct, and we 
tend, as a rule, to prefer things that we can understand. At 
least such appears to be the process in judgments of low 
dermal stimuli, so far as the writer's introspection justifies 
any a priori hypothesis. 

But there are also positive as well as negative reasons for 
considering the phenomena of dermal pain to be most readily 
intelligible on the hypothesis which regards pain as a distinct 
sensation rather than as a quale or a psychic element of all 
states of consciousness. In the first place, pain has a 
peculiar quality of its own, and may occur unaccompanied 
by any other sensory element. When induced by haptic 
stimulation the consciousness of pain in the part stimulated 
may continue some time after the removal of the stimulus. 2 

But there are other points of difference in the time phe- 
nomena of pain and dermal sensations. If we touch a hot 
object the sensation of contact precedes that of pain. 3 Leh- 
mann explains this by the difference in the reaction-times for 
sensations of touch and temperature. 4 The same phenomena, 
however, occur when the pain producing stimulus is not 
heat but pressure. 5 If a needle be suddenly pressed into the 
skin a secondary pain will appear after the sensation of pres- 
sure. In our experiments on the pain threshold for impact 

1 Cf. Dessoir, op. cit., 186. 
3 See Chap. VII, Sec. 2. 
* Cf. Dessoir, op. cit., 201, 324. 

*Lehmann, Die Hauptgesetze des mensch. Gefiihlsleben, 44, 45. 
5 Cf. Goldscheider, Physiol. Gesell., Oct., 1890; Die Lehre der Specif. Energien 
der Sinnesorgane, 1881. 



26 ' SENSATIONS FROM PRESSURE AND IMPACT. 

stimuli the same time relation was observed. 1 Marshall 
argues that the pain consciousness appearing under these 
conditions is not necessarily a new sensation, but a sensa- 
tion x in a painful phase. 2 But is this not to reduce a 
known state of consciousness to one that is unknown and 
only assumed? The same criticism, we will remark, maybe 
made of the explanation generally given of pains arising 
from pathological processes in the internal organs and in the 
muscular and nervous tissues. 

Apart from introspective and experimental evidence, the 
sensation theory of pain is strongly corroborated by dermal 
pathology. It has been known for many years that tactile 
anaesthesia may exist without analgesia, and analgesia with- 
out anaesthesia; 3 and, although hyperalgesia ma}^ be so acute 
that the slighest mechanical jar causes pain, true tactile 
hyperaesthesia is unknown. 4 

The different facts we have noted above certainly go to 
show that pain and haptic sensations are utterly disparate 
states of consciousness, and that in all probability there is a 
corresponding difference between the physiological pro- 
cesses. In fact, from the time when Schiff made his cele- 
brated experiments many physiologists have believed that 
impulses for pain and touch pass to the brain by different 
paths. Goldscheider claims even to have discovered special 
nerves for pain ; but his results have been questioned. 5 
Wundt explains the physiological and pathological experi- 
ments by the altered excitability of the sensory nerves after 
passing through the gray matter of the cord. 6 It is possible 
that at least a partial cause of the delay in the appearance of 
pain is the development of pathological processes in the der- 
mal tissues incited by intense stimulation. That the process 
of dermal pain stimulation is somewhat of this nature is made 

1 See Chap. V, Sec. 2. 

2 Marshall, op. cit., 18. 

3 Wundt, op. cit., I, iii ; Funke, op. cit., 297. Other references are given by these 
writers. 

* Richet, op. cit., 219. 

5 Goldscheider, Archiv fur Anat. und Physiol., 1885, Supp. Bd., 87. For criti" 
cism of G. , cf. Lehmann, op. cit. ; also Dessoir, op. cit. 

6 Wundt, op. cit., I, no, 437, 596; Funke, op. cit., 297. 



THE INTENSITY OF STIMULA TION. 2J 

probable by an observation of Goldscheider. According to 
this writer the delay in the appearance of pain upon stimu- 
lation of the foot of a person afflicted with some disturbance 
of the circulation in that part decreased appreciably as the 
diseased tissues were recovering to their normal condition. 1 
That the delay is due, at least in part, to peripheral pro- 
cesses is also borne out by our own observations. In the 
course of experiments on the pain threshold for impact 
stimuli, the writer has observed pain in the part stimulated 
nearly an hour after the completion of the experiments. 
And again, when pain was induced only after long continued 
pressure, it would continue several seconds after the removal 
of the stimulus. 2 But whatever physiological hypothesis be 
accepted, there seems no doubt that there is a qualitative 
physical difference in function corresponding to the qualita- 
tive psychical difference in sensation. 

Sec. 7. The Quality and Intensity of Sensation. 

In the above discussion we have used the terms quality 
and intensity as applied to sensation. These terms have 
been almost universally used to denote fundamental attri- 
butes of sensation. 3 They are, however, seldom defined. 
The term intensity is generally used in the sense of that 
property of sensation which is functionally related to the 
intensity of the stimulus. If, as some have been led to 
believe, states of consciousness cannot be treated quantita- 
tively, the term as applied to sensation clearly cannot be 
used in such a sense. Such a use is, however, implied in 
the word, since it carries with it the idea of physical quan- 
tity measurable in terms of space, to which all physical 
measurements are reducible. But if we reject the term 
altogether, applying only the predicate qualitative to sensa- 
tional changes, in what way shall we describe subjective 
changes that are discontinuous, as opposed to those which 
are continuous? On the other hand, it may be said that, if 
the term quality be thus restricted, we shall have no means 

1 Goldscheider, Deutsch. Med. Wochenschrift, 1890, no 31. 

2 See Chap. VII, Sec. 2. 

3 Cf. Wundt, op. cit., I, 332 ; Ladd, op. cit., 356; Stumpf, Tonpsychologie, I, 350. 



28 SENSA TIONS FROM PRESSURE AND IMPACT. 

of distinguishing continuous sensational changes due to- 
intensive variations from those due to non-intensive varia- 
tions in the stimulus. But we do not think that there is 
necessarily such a difference in these modes of subjective 
change. The difference may be rather one of perception. 
The sensational change as haptic stimuli are altered in area, or 
as auditory stimuli are altered in pitch, is as much a contin- 
uous, and, we think, quantitative, change as is that caused 
by intensive variations in haptic and auditory stimuli,. 
We are, perhaps, accustomed to think of intensive sensa- 
tional differences as being measurable, rather than non-inten- 
sive differences, simply because it is a matter of familiar 
experience that the corresponding changes in the stimulus 
are quantitative changes, and we are accustomed to estimate 
the magnitude of the stimulus by the changes in sensation. 
If this view be correct, we have no term to apply univer- 
sally to those changes in sensation that are continuous, as 
opposed to those that are discontinuous. For from the 
use of the term intensity in physical science it would be 
difficult to extend its meaning so as to cover those changes 
in sensation that are independent of the intensity of the 
stimulus. 



CHAPTER III. 

The Discrimination of Weights Without Effort and 
the Intensity of the Stimulus. 

Sec. i. Preceding Investigations. 

The comparative ease with which the intensity of haptic 
stimuli can be measured renders the relation between the 
accuracy of discrimination and the intensity of the stimulus 
an attractive field for investigation. In fact, it was upon 
experiments with weights that E. H. Weber based his famous 
generalization. These experiments were, however, too few 
and inaccurate to base a quantitative conclusion upon them. 
By simultaneous pressure stimulations Weber found the 
least noticeable difference for 32 oz. to be 15 oz. and 10 oz., 
or about \ and \ of the stimulus, for the two observers. 
For 32 dr. the least noticeable difference for the same observ- 
ers was found to be 8 dr. and 10 dr. or about \ of the stimu- 
lus. When the stimuli were applied in succession, the least 
noticeable difference was found to be -^ to -fa of the stimulus, 
but Weber does not say what intensities were used. 1 

The next research of importance is that of Dohrn, who 
applied the method of least noticeable difference to the 
investigation of the discrimination of weights of low inten- 
sities. 2 Dohrn found that for the volar surface of the right 
hand a weight of 1 g. had to be doubled in order for a dif- 
ference to be perceived. These experiments were made on 
himself, and also on a boy of eleven, and must, therefore, be 
considered as of little quantitative value. 

A series of experiments with impact stimuli conducted 
by Biedermann and Lowit is described by Hering, who 

1 An account of these experiments in more detail is found in G. E. Muller, Grund- 
legung der Psycho-physik, 189. Weber's original work is inaccessible to the writer. 
3 Dohrn, Zeitschrift filr Rat. Med., 3* R., X, 339. 

29 



30 SEiVSA TIONS FROM PRESSURE AND IMPACT. 

states that they do not conform to Weber's law. 1 The 
method of least noticeable difference was used, and this is 
sufficient to discredit the results, not to speak of the absence 
of information as to the other details of the experiment.. 
In experiments on lifted weights by the same experimenters,, 
the least noticeable difference for 450 g. is stated to be \ g., 
whereas for 500 g. it is given as -^ of the stimulus, a result 
that throws suspicion on the accuracy of these as well as the 
other experiments. 

The most systematic investigation of the subject is that 
of Merkel, who found the least noticeable difference at 50 g. 
to be -^ of the stimulus, and to be fairly constant up to 
2000 g. 2 In these experiments the pressure was exerted 
upon the finger by the arm of a balance constructed for the 
purpose. The muscular reaction of the finger may, there- 
fore, have affected the judgment. That this was the case is 
extremely probable, since Merkel's results closely corre- 
spond with those of the most accurate researches on lifted 
weights. 3 Then, too, Merkel's experiments were made on 
himself, and, as in all such experiments, the knowledge of 
the objective relations of the weights could not but have 
influenced the observer. 

In an interesting series of experiments by Hall and 
Motora, the least noticeable difference was found for from 
5 g. to 200 g. by changing the pressure at the rate of y^- of 
the stimulus per second. 4 From 5 g. to 30 g. this quantity 
was about \ the stimulus, after which it increased consider- 
ably. In these experiments the time relations were such 
that the results could not be compared with those based on 
experiments in which successive stimulation is applied. The 
fact that the intensity of pressure sensations decreases rap- 
idly, at least for low intensities, after the application of the 
weight, makes the problem one of considerable perplexity. 5 

We know of no other work on the subject to the record 

1 Hering, Sitzungsber. der Wiener Acad., 3 te Abth., LXXII, 342, as given ia 
Muller, op. cit., 200. 

2 Merkel, Philosophische Studien, V, 253. 

3 Cf. Fullerton and Cattell, op. cit., 122; Merkel, op. cit., 261. 

4 Hall and Motora, Amer. Journ. of Psy., I, 72. 

5 See Chapter VII, Sec. 1. 



THE DISCRIMINATION OF WEIGHTS WITHOUT EFFORT. 3 I 

of which we have access, 1 except that of Pierce and Jastrow.* 
In this research the probable error for 250 g. was found to 
be ^-g- of the stimulus, and to be further decreased by prac- 
tice. The relation of the probable error to the magnitude 
of the stimulus was not considered. In these experiments 
the pressure was exerted through the muscles, and therefore 
it is probable that, as in Merkel's experiments, the discrimi- 
nation for effort is what is measured. 

Sec. 2. Further Experiments : Method of Procedure. 

There being no satisfactory determination of the accuracy 
of discrimination for objective, as opposed to subjective 
pressure, a series of experiments was made in the following- 
way. The left hand of the observer was placed on the table,, 
comfortably supported, and in such a manner that the palm, 
which was turned upward, was fairly level. The eyes of the 
observer being closed, two weights were placed successively 
upon the hand, and the observer was required to judge which 
was heavier by the method of right and wrong cases. When 
no difference was perceived the observer was required to 
guess. The stimuli with the smaller areas were placed on 
different parts of the region covered by the large area. The 
place was constant, however, for every two compared. The 
degree of confidence was recorded by having the observer 
use four letters, a, b, c and d, according to his confidence.. 
The apparatus used is shown in the accompanying cut. 

The weights used were cylindrical boxes, B, filled with 
shot, the sides being built up when necessary by stiff paper. 
To the bottom of the box was affixed a projecting piece of 
the shape of a fustrum of a cone, N, the base of which came 
in contact with the skin. In this way a small area of stimu- 
lation could be obtained. The material in contact with the 
skin was thick cardboard, so that the influence of tempera- 
ture was practically excluded. Projecting upward from the 
centre of the box was an iron rod, AC, which, on being 
inserted within the glass support, M, of a chemist's stand, S, 

1 We have not access to the dissertation of Bastelberger, Exper. Priif. der zu 
Drucksinn angewandten Methoden, Stuttgart, 1879. 

2 Pierce and Jastrow, National Academy of Sciences, 1884, III, 75. 



32 



SENSA TIONS FROM PRESSURE AND IMPACT. 



prevented the weight from tipping over, as it would other- 
wise have done when the smaller area of stimulation was 
used. The weights were, of course, always placed so as to 
be as nearly as possible perpendicular to the hand. In order 
to obviate slight differences in the surface applied, the same 



A 



M 



i 



B 



•c 



NV 
D 



Fig. 4. 



box was used to give the variable and the standard stimulus. 
The increment of weight consisted of a bag of shot which 
could be placed in the box without being noticed by the 
observer. The stimuli applied were as described above, 
except that having a weight of 3200 g. This consisted of 
three cylindrical kilogram weights placed one over the other. 
Through these weights ran an iron rod, which served as a 
support as with the other weights. To the base was affixed 
a small box loaded with shot, so as to make a total weight of 
3200 g. The base consisted of circular cardboard. The 
time relations were fairly constant. The careful application 
and removal of the weights by the experimenter made it im- 
possible to have the times of application and the intervals 
between the stimulations as constant as might be desired. 
It was found, however, by having the observer note these 
times, that they did not vary appreciably from 2 sec. and 
3 sec. respectively. Moreover, the judgment of weight 
seems to be easiest as soon as the hand receives the full 
force of the weight , and the accuracy of discrimination does 
not vary appreciably when the interval between the applica- 



THE DISCRIMINATION OF WEIGHTS WITHOUT EFFORT. 33 

tion of the two stimuli is not greater than 10 sec. 1 No fixed 
order was used in applying the stimuli, the only require- 
ment being that for a series of ioo experiments in 50 the 
second weight should be heavier, and in the other 50 lighter. 
About 10 sec. intervened between two successive experiments, 
but no effort was made to have this constant. At one sit- 
ting 20 or 25 experiments in a given series were made. Then 
the observer rested a few minutes, and another set of experi- 
ments was made. The time devoted to the experiments at 
one sitting varied generally from an hour to an hour and a 
half. In order that the influence of fatigue might be the 
same for the different intensities used, the order in which 
the different sets of experiments for the different series was 
made was varied, so that a given intensity would be used as 
much in the first as in the latter part of the sittings. The 
observers were students of Psychology, with some previous 
practice in experimental work. 2 The experiments were be- 
gun in March, 1892, and completed in June, 1893. 

With regard to possible sources of error, most of them, 
we think, were eliminated. In applying the weights with 
the hand, it is impossible to control properly the velocity of 
impact. The writer endeavored to obviate this difficulty by 
applying the weights slowly and carefully. In this way the 
error may be neglected for weights of sufficient intensity to 
cause a distinct sensation of pressure apart from one of 
impact. For weights of 100 g. and 200 g., however, the 
depression of the skin due to the pressure is so slight that 
impact cannot be entirely neglected. The rate of applica- 
tion was, however, kept as constant as practicable. Then, 
as is shown in Chapter V., the discrimination of weights by 
impact is about the same as by pressure. 3 

Another source of error lies in the slight variations of 
the weight from a perpendicular position and consequent 
pressure upon the glass support. For the purpose of inves- 

1 Cf . Weber, op. cit., 545, where it is stated that there is no appreciable differ- 
ence in the accuracy of discrimination after an interval of 30 sec. A far more accurate 
investigation of the matter is that of Fullerton and Cattell, op. cit., 148. 

2 The writer would take this occasion to express his appreciation of the kindness 
of those who have devoted so much time to these and other experiments, and to ex- 
press his gratitude for the assistance so generously given. 

3 See Ch. V., Sec. 4. 



34 SENSA TIONS FROM PRESSURE AND IMPACT. 

tigating this 'source of error, a formula was deduced for the 
decrease in the amount of pressure exerted upon the hand 
when the weight was not perpendicular. If C be the centre 
of gravity of the mass, D the point of application, the area 
being, for convenience, considered inappreciable, A the 
point of application of the rod upon the glass support, W 
the weight, and S the angular deviation from the perpen- 
dicular of the line through C, D and A ; then for the loss of 
weight at D, which we shall call x, we shall have, 

x = Wsin 2 <£-^ 

In this formula it is assumed that at the point A there is 
such friction that the mass is not free to move. By observ- 
ing what appeared to be approximately the maximum value 
of <j> in the experiments, the corresponding value of x for a 
weight of 500 g. was found by the formula to be 1.2 g. An 
experimental determination of this quality was also made 
by means of the balance. A 500 g. box with sharpened base 
was placed in the pan, so that the rod in contact with the 
glass support deviated from the perpendicular to about the 
same extent as that which was found to be the maximum de- 
viation in the experiments. The loss of weight was found to 
be 1.5 g. Inasmuch as the measurement was rendered inex- 
act by the horizontal component of the pressure exerted, 
the result corresponded as closely as was expected with that 
obtained by calculation. The true loss of weight was, how- 
ever, much less than this for the stimuli used ; for the place 
of application having considerable area, it is evident that the 
weight will tend to be in more stable equilibrium. Then 
the true error is not the average loss of weight, but the 
variation from this average, which is of course much less. 
We may, therefore, neglect this source of error entirely. 

In every set of 100 experiments, in 50 of which the 
second weight was lighter and in 50 heavier, the percent- 
age of right answers was calculated for both groups of 50 
answers. The accuracy of discrimination, h, was deter- 
mined from these data by tables based upon the well-known 
formula: 

- = I + -7= j e - t2 dt 
n v 7r«y 



THE DISCRIMINATION OF WEIGHTS WITHOUT EFFORT. 35 

In the tables used 1 the values of were given, instead 

of those of hA, P.E. being the probable error, or that 
error which would be equal to A, when the percentage of 
right cases is 75. Tables giving the values of hA may be 

readily changed so as to give the values of p-w- by substi- 

tuting for h the expression p '* . In some of the series it 

was found that the constant error, or tendency to overesti- 
mate the second stimulus, was so great that the use of a 
larger increment was necessary when the second weight was 
lighter. For otherwise the second weight would have been 
judged heavier the great majority of trials ; and the observer, 
therefore, would have acquired the habit of judging the 
second weight the heavier, which would have vitiated the 
experiments. This involved the use of special formulae, 
which we now give. C.E. is the constant error, P.E. the 

probable error, T x the value in the table for p p when the 

second weight is lighter, T h the value when it is heavier, 
and A h and A 1 are the increments used when the second 
weight is heavier or lighter. 

Case I. 

When no constant error occurs, real or apparent, A h = 
Aj == A, and T h = T Y = T. Then 

A 



P.E. 
whence, 



= T, 



P.E. = 7=p. 

Case II. 

When a constant error occurs, and only one increment is 
used, we have, 

1 Given by Fullerton and Cattell, op, ciU, 16. They will also be found, in different 
form, in Philosoph. Studien, IX, 145 ; and in Fechner, Elemente der Psychophysik y 
II te Auf., Leipzig, 1889, 108. 



p.E. = ,p , ,p , and C.E. =T h P.E. 



36 SENSA TIONS FROM PRESSURE AND IMPACT. 

A + C.E. A - C.E. ~ 

P.E. = lhand P.E. - iv 
whence, 

2 A 
T k +iy 

Case III. 

If a constant error occurs, and A h is > A l or < A„ we have, 

P.E. = fc + ft , and C.E. = T h P.E. — A h . 

Case IV. 

If both stimuli are equal when the second is judged 
heavier, i. e., if A h = O, we have, 

PE ^— 

and 

C = P.E. T r 

Case V. 

If the first stimulus is greater than the second, when the 
second is judged heavier, A h is minus, and we have, 

-A h + C.E. _ 
P.E. "" h ' 



and 



A, - C.E. T 
P.E. ~ lJ 



whence, 
and 



P.E. = 



_A-a 



h 



T h + T,» 

C.E. = P.E. T h + A„. 

Case VI. 

If the conditions are the same as in Case V., but — <-&V 

when the second weight is judged lighter, calling the value 

of the probability integral corresponding to 100 , T, 1 , we 

have 

C.E. -A h _^ 
P.E. ~~ h ' 



THE DISCRIMINATION OF WEIGHTS WITHOUT EFFORT. 37 

and 



whence, 
and 



C.E.-A ,, 

P.E. — ±l ' 

PE - ^-A 

C.E. = P.E. T h + A h . 

Case VII. 

If the conditions are the same as in Case VI., except 
that no increment is used when the second weight is judged 
heavier, we have 

P.E. =. A ' 



T — T 1 

and 

C.E. -=T h P.E. 

Case VIII. 

If the conditions are the same as in Cases VI. and VII., 
except that for the second to be judged heavier, an incre- 
ment is used, + A h , we have 

PE -^L±A 

and 

C.E. = P.E. T h -A h . 

By the above formulae were calculated the values of P.E. 
and C.E. for each set of ioo experiments. 1 That under Case 
II. was used in the great majority of the calculations. Such 
increments were generally used as would give a percentage 
of right cases as near as possible to 84 per cent., since fewer 
observations are needed for such a value of A in order to 
calculate the value of P.E. 

The value of P.E. thus found is not strictly that for the 
standard stimulus, but is compounded of this and its value 

1 In order to test the approximate accuracy of the formulae, the value for C.E. thus 
found was added to the second stimulus, and it was noted whether the conditions were 

such as to give about the value of —as expected from the value calculated for P.E. 



38 SENSATIONS FROM PRESSURE AND IMPACT. 

for the variable stimulus. 1 When the increment is very 
small this error may be neglected. But in some of our ex- 
periments, on account of the magnitude of the constant 
error, an increment was used of from \ to -§- of the stimulus. 
This difficulty cannot be overcome unless the relation of the 
probable error to the stimulus is known. Inasmuch as we 
found that this relation was approximately that demanded 
by Weber's law, at least within certain limits, we corrected 
the values of P.E. on this assumption. The result will at 
least be more correct than it would if such a correction were 
not made, even if the probable error increased more slowly 
than is assumed. To make such a correction, let S be the 
standard stimulus, P.E. the probable error obtained from 
the formulae above given, and P.E. X the value of P.E. cor- 
rected for the standard stimulus. Then P.E. may be con- 
sidered as approximately the arithmetic mean of the proba- 
ble errors for the stimuli used. We shall have, therefore, 



P.E. 



whence, 



P.E., + P.E., ( S + A -> + P.E., ( S - + A '> 



4S 



P.E. X =P.E. f c , 4 5* , A ) 

\4S-f-A h + A 1 / 



Sec. 3. Results. 

The values of P.E. given in the tables below are the cor- 
rected values. In the majority of cases they do not differ 
appreciably from the uncorrected values, but at times the 
difference is considerable. No correction was made for the 
constant error, since its relation to the magnitude of the 
stimulus is more complex. 

In the appended tables the standard stimuli used are 
given in the first column. Then follow the different proba- 
ble errors for each set of 100 experiments, 2 P v P 2 , etc., and 
their averages and mean variations. The other columns 
give the different constant errors, C v C 2 , etc. 

1 Cf. Muller, op. cit.. 21 

• The probable errors for N. F. and J. S. are based upon 80 experiments. 



THE DISCRIMINA TION OF WEIGHTS WITHO UT EFFOR T. 39 

Observer, N. F. ; area, 8 cm. 



s 


Pi 


P2 


P3 


P 4 


Av. 


M. V. 


Ci 


C 2 


c 3 


c 4 


Av. 


M. V. 


200 


3 1 


21 


16 


21 


22 


4- 


17 


17 


16 


17 


17 


0. 


800 


255 


138 


72 


86 


137 


59 


120 


164 


176 


J 59 


155 


17 


l600 


I 9 I 


221 


185 


175 


*93 


18 


J 57 


i43 


280 


200 


*95 


43 


3200 


341 


474 


— 


— 


408 


44 


119 


222 


— 


— 


170 


57 



Observer, J. 


S. ; area, 8 cm. 










S 


Pi 


P 2 


Av. 


M. V. 


Ci 


& 


Av. 


M. V. 


800 


134 


97 


115 


18 


11 


30 


20 


9 


1600 


I48 


207 


177 


28 


5i 


100 


75 


24 


3200 


244 


261 


252 


8 


149 


121 


1 3S 


14 



Observer, 


R.; 


area, 8 cm. 












S 


Pi 


p 2 


P 3 


Av. 


M. V. 


Ci 


C* 


c 3 


Av. 


M. V. 


100 


25 


27 


J 9 


23 


3 


17 


16 


37 


23 


9 


500 


I02 


121 


83 


102 


1 3 


70 


120 


166 


119 


32 


1500 


248 


337 


229 


271 


43 


63I 


799 


682 


704 


63 



Observer, 


McW. ; 


area, 8 


cm. 
















S 


Pi 


Pa 


P 3 


P 4 


Ps 


Av. 


M. V. 


Ci 


Ca 


c 3 


c 4 


c 5 


Av. 


M. V. 


100 


20 


24 


24 


14 


16 


r 9 


3 


I 


O 


15 


5 


2 


4 


4 


500 


33 


42 


31 


40 


33 


3^ 


4 


-13 


-13 


2 


-24 


2 


-9 


9 


1500 


no 


I30 


no 


100 


109 


112 


7 


6 


9 


6 


18 


12 


10 


4 


3200 


233 


183 


156 


196 


197 


193 


19 


96 


286 


200 


233 


285 


218 


56 



40 SEJVSA TIONS FROM PRESSURE AND IMPACT. 

Observer, L. S. ; area, 8 cm. 



s 


Pi 


P» 


P3 


P4 


Ps 


Av. 


M.V. 


Cx 


C* 


c 3 


c 4 


Cs 


Av. 


M.V. 


IOO 


17 


20 


17 


19 


16 


18 


1 


-4 


-3 


1 


6 








3 


500 


37 


29 


39 


42 


47 


39 


4 


-12 


—2 


-6 





-11 


-6 


3 


1500 


114 


100 


114 


103 


in 


108 


5 





67 


13 


57 


69 


41 


28 


3200 


243 


217 


256 


206 


243 


233 


17 


85 


195 


125 


70 


239 


i43 


59 



Observer, L. S. ; area, -fe cm. 



s 


Pi 


P2 


Ps 


P4 


Ps 


Av. 


M.V. 


Ci 


c* 


c 3 


c 4 


C 5 


Av. 


M.V. 


100 


9 


14 


13 


16 


16 


13 


2 


1 


—I 


1 


1 


4 


1 


1 


500 


43 


29 


35 


57 


41 


41 


7 





—2 


-14 


17 


J 9 


4 


8 


1500 


124 


9 1 


127 


105 


105 


no 


11 1 59 


49 


in 


74 


74 


73 


15 



Observer, N. F. ; area, ^ cm. 



s 


Pi 


Pa 


P3 


P4 


Av. 


M.V. 


Ci 


c* 


c 3 


c 4 


Av. 


M.V. 


200 


36 


77 


— 


— 


56 


20 


48 


3° 


— 


— 


39 


9 


800 


87 


121 


120 


125 


11 3 


12 


i95 


146 


65 


70 


119 


5i 


1600 


227 


231 


196 


158 


203 


26 


259 


263 


215 


*33 


217 


44 



Observer, J. S. ; area, -^ cm. 



s 


Pi 


Pa 


Av. 


M.V. 


Ci 


C* 


Av. 


M.V. 


800 

1600 


IO4 
221 


IO3 
171 


103 
196 




25 


-26 

94 


-26 



-26 
47 



47 



THE DISCRIMINA TION OF WEIGHTS WITHO UT EFFOR T. 4 1 



These results are graphically represented in the accom- 
panying curves. 




SQQ 1500 

Fig. 5 — Large Area. 



5^St 



im. 




soo 
Fig. 6 — Small Area. 



Stir* 



In the above experiments no stimuli were used less than 
ioo g. Less extended experiments were made on S. F., an 
excellent observer, for a standard stimulus of 5 g., the varia- 
ble stimulus being 7 g. The stimuli used were cylindrical 
pieces of lead. To the bottom was fastened a circular piece 
of cardboard, having a diameter of 1.5 cm. The weights 
were carefully lowered upon the palm of the hand by iron 
rings projecting from the tops. Below are the values of the 
three probable errors obtained for each set of 100 experi- 
ments, and also the value of the average divided by the 
mean of the stimuli used. 



Observer, S. F. 
Stimulus. P x 
S g. and7g. 3.7 



A 2 
1.8 



x 3 
2.0 



Av. P. 

2.5 



S 
P 

•4 



42 SENSA TIONS FROM PRESSURE AND IMPACT. 

These results may be taken as representative for good 
observers, since the probable error for S. F. at iooo g., and 
with the same area, was found by 200 experiments to be 
about y 1 ^ of the stimulus, which is fairly typical. 

It is evident from the above results that Weber's law 
holds fairly well between the approximate limits, 300 g. and 
3000 g. For very low stimuli the probable error increases 
much more slowly than the stimulus. For high intensities 
it increases somewhat more slowly, though the deviation is 
not very marked. It is probable that observers differ some- 
what not only in their absolute accuracy of discrimination, 
but even in the relation of this accuracy to the magnitude of 
the stimulus. This is shown in the curves for L. S., J. S., 
and McW. (Figure 2), that of J. S. clearly departing from 
the straight line demanded by Weber's law. The irregular 
shape of N. F.'s curve is perhaps to be explained by the 
decided variation in his accuracy of discrimination, as shown 
in the tables. If it be assumed that such variation is the 
cause of the irregularity of the curve, it is evident that for 
this observer the probable error increases in direct propor- 
tion to the stimulus within the limits used. 

Summarizing the quantitative results obtained, the maxi- 

P E 

mum value of — W-' for a set of 100 experiments was J, 1 the 

minimum -j^, 1 and the average for all observers and all inten- 
sities above 100 g. was -1-. 

It is evident that individuals of about the same age and 
social class differ somewhat in their discrimination. Of the 
eight observers tested only two showed much variation from 
the average, N. F. and R. having as their relative probable 
errors \ and \. From both of these observers the writer 
would have expected at least as good results as from others. 
Both complained of a tendency to drowsiness in the course 
of the experiments, and to this their low accuracy may per- 
haps be ascribed. 

1 Calculations based upon only ioo experiments are, of course, somewhat affected 
by the variable error. 



THE DISCRIMINA TION OF WEIGHTS WITHO UT EFFOR T. 43 

Sec. 4. The Constant Error. 

It has for many years been known that in comparing two 
stimuli applied successively, there is in general a tendency 
to overestimate the second. In no instance known to the 
writer has a constant error of such magnitude been observed 
as those shown in the records of R. and N. F., which were 
for some stimuli as great as \ of the stimulus. The value of 
C. E. seems to increase with the stimulus, but not in direct 
proportion. It is very small or even negative for low inten- 
sities, but increases rapidly, apparently soon reaching a maxi- 
mum. Some persons do not show any constant error except 
for very high intensities. Experiments on L. F. showed no 
constant error for 1000 g., 1 but at 3200 g. it was appreciable. 

Persons having a large constant error tend to have a large 

probable error. This is shown by the following average 

P F C E 

values, in round numbers, of g and — U— - for 8 persons. 

L. F. 1 S. F. 2 McW. L. S. J. S. W. 2 N. F. R. 

Av 1 1 1 11111 

^ V * g UriTT HTTTT¥¥TT 

Av - -%-' t zer °] t zer °] A A A A A \ 

Whether the constant error influences the probable error 
or vice versa, we cannot say. Possibly these magnitudes are 
causally related to some process affecting them both. 

The constant error appears to vary more than the proba- 
ble error. Below are given the relative mean variations of 
the probable and constant error. They are calculated by 
taking the mean of the values of the mean variation divided 
by the probable or constant error, as the case may be. We 
give also, for the sake of comparison, the average value of 
P.E. 



S 



for the different observers. 



1 See Chapter V, Sec. 5. 

2 The experiments on W., L. F. and S. F. will be given in Chap. V., Sec. 4, and 
Chap. VI., Sec. 5. The standard stimulus was not varied, being 200 g. for W. and 

1000 g. for L. F. and S. F. 



1 


1 


1 
T 


1 


1 


2 
7 


1 


i 


1 


1 


3 


1 


\ 


i 


1 


tV 


1 


1 



44 SENSA TIONS FROM PRESSURE AND IMPACT. 

N.F. J.S. R. L.S. McW. W. 
M.V. 
P.E. 
M.V. 
C.E. 
P.E. 
S 

Since there is in general greater variation in C.E. than 
in P.E., we conclude that these variations are to some 
extent true variations rather than chance variations due to 
the conditions of the experiment. The variation of the con- 
stant error was most noticeable in the case of an observer, 
E. G., on whom in two weeks over 500 experiments were 
made. In these experiments the value of C.E. increased so 
rapidly that no calculations could be made. At first it was 
inappreciable for 100 g., 500 g. and 1500 g. ; but it increased 
with practice until for 100 g. it was apparently as great as 
the stimulus, and for the higher intensities from \ to \ as 
great. The theoretical importance of these variations lies 
in the application of the probability integral to the method 
of right and wrong cases, for in this integral P.E. and C.E. 
are assumed to be constant. 

If the constant error be due to central processes, we 
should expect individuals having a great error for pressure 
to have a similarly great error for lifted weights. But this 
is not the case. R., who had the greatest C.E. of all the 
observers, failed to show the slightest trace of any overesti- 
mation in forty experiments with lifted weights. L. S. and 
McW. likewise had no appreciable C.E. for lifted weights of 
high intensity, though they had for pressure stimuli of high 
intensity. Not only this, but a constant error for pressure 
does not apparently involve one for impact. At least in 25 
experiments on R., no C.E. was appreciable for 50 g. falling 
20 cm. 

Sec. 5. The Confidence of the Observer, 

The confidence of an observer in estimating stimuli not 
differing greatly, varies from complete doubt to complete 
certainty. The degree of confidence depends upon the mag- 



THE DISCRIMINA TION OF WEIGHTS WITHO UT EFFOR T. 45 

nitude of the difference of the stimuli, and consequently 
upon the probability of correctness. 1 

In the experiments on the discrimination of weights, ob- 
servers were requested to say a when certain, b when fairly 
confident, c when less confident and almost doubtful, and d 
when unable to decide except by guessing. The results for 
different observers are now given. The figures indicate the 
percentages of times the different letters were used when 
the observer was right and also when he was wrong. 

McW. 

a. b. c. d. 

r. 14 per cent. 44 per cent. 37 per cent. 5 per cent. 

w. 4 " 29 " 55 " 12 " 

L. S. 

r. 1 per cent. 17 per cent. 73 per cent. 9 per cent. 
w. — 3 " 70 " 27 " 

R. 

r. — 13 per cent. 78 per cent. 9 percent. 
w. — 6 " 78 " 16 " 

J. S. 

r. — yy per cent. 92 per cent. 1 per cent, 
w. — 22 " 98 " — 

N. F. 

r. 2 per cent. 24 per cent. 66 per cent. 18 per cent, 

w. 8 " 27 " 59 " 6 " 

As the percentage of right cases varied for different ob- 
servers, we cannot express their degree of confidence by the 
percentage of times a and b were used. We may, however, 
use as a rough indication of individual differences the fraction 

— , that is, the ratio of the number of times he was confident 
w 

when wrong to the total number of times he was wrong. 

This fraction is for L. S. only y^^; for R., yJg-^; for 

McW., T \V; for J. S., jfo; and for N. F., &\. By com- 

1 In experiments on lifted weights described by Fullerton and Cattell, the degree 
of confidence varies nearly as the percentage of right cases. Op. cit. y 126. 



46 SENSA TIONS FROM PRESSURE AND IMPACT. 

paring these numbers with the relative probable errors,* 
we see that there is no relation between the two quantities. 2 
As will be seen from the above results, the observers were 
seldom certain. It is remarkable, however, that two ob- 
servers were certain 4 per cent, and 8 per cent, of the time 
respectively when they were wrong. We might suppose 
that the probability of correctness when confident would be 
inversely related to the degree of confidence, as shown by 

c 
the fraction — above mentioned. This does not appear to 
w rr 

be the case. For McW. and J. S. the probability of cor- 

rectness when confident was -A 3 ; but the values of — for the 

1U w 

two observers were quite different. 

The number of times the observers were correct when 

guessing was greater than could be explained by chance. 

By taking the number of d's in ten separate sets, of from 

100 to 150 each, and computing the percentage of right cases, 

it was found that in all of these ten sets this percentage was 

over 50 per cent., the average being 59 per cent. 4 From 

this it follows that to halve the number of doubtful answers 

and add this to the number of right cases, as has generally 

been done, is an illegitimate method of procedure, since 

based on an erroneous assumption. In the case of some 

observers whose confidence was small, this percentage ran 

as high as 65 per cent, and 70 per cent. The bearing of this 

on the method of least noticeable differences is, we think, 

quite obvious. F., about 70 per cent, of whose guesses 

were correct, stated explicitly that when guessing he felt no 

difference whatsoever, and that his judgment was entirely a 

guess. But apart from problems of method, such facts are 

of not a little theoretic importance, since they show clearly 

the possible accuracy of unconscious mental processes. 

1 See vSec. 4 of this chapter. 

2 Fullerton and Cattell found, contrary to this, that observers having the largest 
probable errors had the greatest confidence. Op. cit., 126. 

3 This corresponds with the results of Fullerton and Cattell for lifted weights, 
T 8 (f 7 being the average probability of correctness when confident for ten observers. 

4 Sixty per cent, is that given by Pierce and Jastrow, op. cit. ; Fullerton and Cat- 
tell give 60 and 65 per cent, for two observers, op. cit., 132. 



CHAPTER IV. 

The Place of Stimulation. 

Sec. i . Previous Investigations. 

In our study of the accuracy of discrimination we con- 
fined our experiments to a definite area. It has, however, 
been asserted on experimental grounds that the accuracy of 
discrimination varies for different parts of the body. We 
shall now turn to this aspect of the question. 

The so-called tactile sensibility of different parts has gen- 
erally been determined by Weber's aesthesiometer. But by 
this method the spatial sensibility only is measured, and we 
are not justified in assuming that this represents the general 
delicacy of the peripheral end organs. Perhaps the simplest 
method of testing the sensibility of different parts is to 
determine the threshold at these parts. The fact that the 
threshold is not a fixed quantity does not render this method 
impracticable. Aubert and Kammler 1 found by this method 
that there was but little difference between the different parts 
of the body. The face was somewhat more sensitive and 
the foot less sensitive than other regions, and no appreciable 
difference appeared between the sensitiveness of dorsal and 
volar surfaces. The results were quite different for parts 
where the hairs were shaved. Similar results were obtained 
by Bloch, 2 according to whom the face and palm of the hand 
were more sensitive than the trunk, arms and legs when 
shaved. 

A quite different method was used by Goltz, 3 who applied 
to the place of stimulation the end of a rubber tube filled 
with water, the other end being applied to the radial artery. 
The stimulus was the periodic pressure from the arterial 

1 Aubert and Kammler, op. cit. (See Chap. II, Sec. 4.) 

2 Bloch, op. cit. (See Chap. II, Sec. 4.) 

3 Goltz, Centralblatt filr die Med. Wiss., 1863, 273. 

47 



48 SENS A TIONS FROM PRESSURE AND IMPACT. 

pulsations. Goltz concluded that the sensitiveness of the 
skin to pressure stimuli varied in general in the same way as 
the discriminative sensibility for space. The method used 
is, however, extremely unsatisfactory. Not only was no 
quantitative determination made, but possible preconcep- 
tions could not but influence the process of judgment. 
Goltz was led to the use of such a method by observing that 
a branch of the temporal artery can be easily felt with the 
finger, but not with the hand. This apparent difference in 
sensitiveness is, we think, at least partly due to differences 
in the manner of applying the pressure. It is much more 
difficult to feel the arterial pulsations with the dorsal than 
with the volar surface of the finger, but Aubert and 
Kammler, as well as Bloch, found that there is no appre- 
ciable difference in the sensitiveness of the dorsal and volar 
regions. 

A still more novel method is that of Funke, 1 who tested 
the sensitiveness of the skin by applying glycerine solutions 
of different proportions. That solution was determined 
the adhesiveness of which could be just distinguished from 
that of pure glycerine. It is clear that the accuracy of dis- 
crimination is here tested, not the threshold, and that, too, 
in such an inexact manner that accurate quantitative results 
would be impossible. Besides, the stimulus used is traction 
and not pressure, and as would be expected, the results are 
quite different from those obtained by others for pressure. 
Considering the inaccuracy of the method employed, Funke's 
results agree fairly with those of Bloch, 2 for traction stimuli, 
the order of sensitiveness of the principal parts of the body 
being: finger tips, palm of the hand, back of the hand, fore- 
arms, breast, thigh, feet and back. 

Results quite different from those of the threshold inves- 
tigators were found by Schwaner 3 and also by Sergi, 4 who 
determined the rate of vibration of a tuning fork at which 

1 Funke, Fischer's Med. Buchhandlung, 1891, 29, as quoted in Zeit. fur Psy. t 
Vol. 2, 399. 

f Bloch, op. cit. 

8 Schwaner, Die Priifung der Hautscnsibilitdt, Dissert., Marburg, 1890, as quoted 
in Zeit. fur Psy., II, 398. 

4 Sergi, Revista di Filosojia Scientifica, 1891, as quoted in Zeit. fiir Psy., Ill, 175. 



THE PLACE OF STIMULATION. 49 

the tactile sensations began to fuse. Schwaner's results are 
criticised by Sergi, who points out that the amplitude of 
vibration, and consequently the intensity of the stimulus, is 
much greater for forks at low pitch. Sergi concludes that 
we measure the sensitiveness of the different parts of the 
skin by differences in the intensity of the stimulus necessary 
to cause a distinct sensation. It is probable that the threshold 
element enters into the experiment, as Sergi holds ; but as 
the results are quite different from those of Bloch and Aubert 
and Kammler, it is not improbable that local differences in the 
duration and fusion of tactile sensations affect the results. 
Krohn 1 states that dermal after-images last much longer for 
some parts than for others. 

The accuracy of discrimination for different regions was 
investigated by Weber 2 and also by Dohrn. 3 Weber applied 
weights to the forearm, and found that the increment neces- 
sary in order to be appreciated was twice as great as when 
the same weight was applied to the hand. Weber does not, 
however, mention the magnitude of the stimuli used. Accord- 
ing to Dohrn's researches, the method of which has been 
described, the least noticeable difference for a stimulus of 1 g. 
was smallest for the thumb and fingers. Then follow the 
hand, forearm, breast, knee pan and feet. But, as we have 
already noted, these experiments are of little exact value, 
since not only is the method open to serious objections, but 
the experiments were made by the observer on himself. 
Then, too, according to Aubert and Kammler, individuals 
differ not a little in the relative sensitiveness of different 
parts. We cannot assume, however, even if these results 
are accepted, that the absolute accuracy of discrimination is 
measured for different places. As we have seen, the relative 
accuracy of discrimination is much greater for stimuli o£ 
moderate intensity ; consequently, the lower the threshold 
for a given region, the greater would be the accuracy' of 
discrimination at this region for low intensities. 

1 Krohn, Journal of Mental and Nervous Diseases, March, 1893, ii % 
8 Weber, op. cit., 548. See Chap. I, Sec. 1. 
•* Dohrn, op. cit. See Chap. Ill, Sec. 1. 



50 SENSA TIONS FROM PRESSURE AND IMPACT. 

Sec. 2. Further Experiments : the Accuracy of Discrimination,, 

The writer made a few rough experiments on the thresh- 
old sensibility of the hand, arm and face, by the instrument 
already described, 1 and the results corroborated those given 
by Bloch, Aubert and Kammler, as well as Dohrn, assuming- 
that the latter's results were due to the threshold differences. 
Experiments were also made on the discrimination of weights 
by the method of right and wrong cases, the probable error 
being determined for different parts. Six hundred experi- 
ments were made on N. F., the volar surface of the left index 
finger, third phalanx, being the place of stimulation. The 
stimuli used were 50 g., 200 g. and 800 g. The average of 

P E 

the six values of ^ obtained was i 3 ^, which was approx- 
imately the same as that obtained for the palm of the hand 
of the same observer. 2 Experiments were also made on 
L. S. The stimulus was 100 g., and the places of application 
were the volar surface of the left index finger and the back 
of the hand. The probable error for each set of 100 experi- 
ments is given below, as well as that obtained for the palm 
of the hand at the same time. 

^v nn f .r P.E. for palm P.E. for back 

Observer, r.jb. lor finger. t , r , t ,1 , 1 

te of hand. of the hand. 

L. S., 9. 16. 17. 

On account of the comparatively small number of experi- 
ments the probable errors given are considerably affected by 
the variable error. Making allowance for the variable error,, 
the results for L. S., taken together with those for N. F., 
indicate that apart from individual variations there is no 
very marked difference in the accuracy of discrimination for 
moderate intensities at different parts of the hand. 

A further series of experiments was made on S. F. with 
•5 g. and 7 g. as the stimuli. The volar surface of the index 
finger and the hand, and the dorsal surface of the forearm, 
were the places of stimulation. In these experiments the 
^rror due to impact is constant for the different places, and 

1 See Chap. II, Sec. 4. 
;?,Sse€Jbap. HI, Sec. 3. Av. ^~ for N. F. is \. 



THE PLACE OF STIMULA TION. 



5* 



does not, therefore, affect the relative results. Below are 
given the probable errors for the different sets of ioo experi- 
ments. 



/ 


Finger. 


Hand. 


Wrist. 


Stimuli. 


Pi 
i-3 


P 2 


P 3 


Av. 
1.4 


P, 


P, 


Pa 


'Av. 


P t 


P, 


P 3 


Av. 
4-9 


5 g. and 7 g- 


1-5 


i.5 


3-7 


1.8 


2. 


2-5 


9.1 


3.3 


2.3 



These experiments show that for 5 g.-J g. the discrimi- 
nation is somewhat more accurate for the tip of the finger 
than for the palm of the hand, and much more so than for 
the back of the fore arm. The observer improved, however, 
greatly from practice in the experiments on the wrist. As 
the threshold sensitiveness is here much less, and we are not 
accustomed to judging stimuli thus placed, the difference 
was to be expected. 



Sec. 3. The Intensity of the Sensation. 

Another method of investigating the sensitiveness of 
different places is by comparing the intensive effect of a given 
stimulus with that of the stimulus applied to another region. 
Weber found that 5 oz. placed on the finger was judged 
greater than 4 oz. on the arm, but when the weights were 
reversed they were judged equal. 1 In order to obtain more 
accurate results, a weight of 5, 100, or 1000 g. was applied 
to the finger, and upon removal applied to the dorsal surface 
of the wrist, the observer being required to judge which 
seemed heavier. The observers were ignorant of the fact 
that the stimuli applied were the same. If in 10 experiments 
no underestimation of the stimulus was appreciable at one 
of the two places of stimulation, as compared to the other, 
we concluded that any difference in sensitiveness was too 
slight to be considered. When, however, the answers were 
such that the weight when applied to the wrist was consid- 
ered much lighter, increments were added to it until it 
seemed equal to the standard weight applied to the finger. 
When 5 g. was used, increments could not be conveniently 

1 Weber, op. cit. 



52 



SENSATIONS FROM PRESSURE AND IMPACT. 



added, so 7 g. and 10 g. weights of the same area were used 
as comparison stimuli. Below are the results for four ob- 
servers. The values of the increments given are based on 
five experiments. 



Stimulus. 


Increments added on wrist. 


P 


K 


L 


F 


iooog - - - 

ioog - - - 

sg - - - 




50 

>5 










>2<5 


300 
90 

>2<5 



The above results seem to show that there is, at least for 
low intensities, a marked underestimation of stimuli applied 
to the arm, in comparison with stimuli applied to the finger. 
Observers differ greatly, however, that this cannot be stated 
asa universal law, K. not showing any appreciable underes- 
timation. Possibly these individual differences may be due 
to central processes, such as unconscious allowance for sen- 
sory difference in comparing the stimuli. The fact that the 
underestimation tends to diminish for high intensities goes to 
show that different regions of the periphery do not have an 
intensity coefficient as Weber concluded. 

Sec. 4. The Pain Threshold. 

By the algometer already described the writer made five 
measurements of the pain threshold for different parts of the 
body. But one measurement for a given place was made at 
a time.. Below are the results in kilograms, with the prob- 
able errors of the averages. 

Top of the head, parietal region. - 1.8 ±.005 

Forehead, frontal region. - - - - - 1.3 ±.008 

Breast, over sternum. - 2.4ZIZ.006 

Abdomen. - - - - - - - 1.7 ±.006 

Back. 8.0 ±. 010 

Right temporal region of head. - 1.0 ±1.003 

Left " " " - - - - 1.3 i.004 



THE PLACE OF STIMULATION. 



53 



Right thigh, ventral region. - 

Left " " 

Right foot, plantar surface. 

Left an <<---_. 

Right heel. " " 

Left ■ . ' < << ' * - - - 

Right hand, volar surface. - - - 

Left . " " " 

Right hand, dorsal surface. 1 - - - 

Left " " " 

Right index finger, volar surface, 3d phalanx. 

Left " ll " li ■" '* 



3 ±.01 

2 ±.007 

5 ±.009 

4 ±.005 
o ±.006 

9 zb.OI 
3^.007 

2 ±.007 

3 ±.006 

6 ±.01 

5 z+=.oo6 



3 ±.006 

From this it appears that the regions over the frontal 
and temporal bones are most sensitive to pressure, and the 
heel, the back, and the muscular regions of the leg and hand 
the least sensitive. The sensitiveness to pain seems, then,- to 
depend largely upon the thickness of the skin and the extent 
of subcutaneous tissues. The left side of the body is per T 
haps slightly more sensitive than the right side> but the. dif- 
ference, if any exists, is hardly appreciable. .. 

J The measurements on the hand were carried on simultaneously with the others. 
But quite a number of experiments had been made on the hand before, and it seemed 
to have become less sensitive by about 2 k. than when it was first tested. 



CHAPTER V. 



Sensations of Impact. 

Sec. i. The Threshold 1 - for Touch. 

We should expect a priori that a given weight would have 
greater effect if applied with appreciable impact than if impact 
were excluded. In order to find if such were the case, a 
circular piece of cardboard was placed carefully upon the 
hand of the observer, being suspended by a delicate brass 
wire about i cm. long. The whole weighed .01 g. S. F. and 
the writer served as observers, the one not acting as observer 
placing the stimulus. The observer's eyes were closed, and 
he did not know when the stimulus was applied. Fifty ex- 
periments were made on both observers, and the number of 
times they perceived the stimulus was recorded. In order 
to compare the results with those obtained when impact was 
excluded, the pressure was applied by means of the instru- 
ment described in Chap. II, Sec. 4. In order to have the 
area of stimulation constant, the pressure was exerted upon 
the card piece to which reference has just been made, the 
projecting wire handle having been removed. The pressure 
thus applied was .4 g. Below are given the percentage of 
times the stimuli was felt in 50 experiments. 





Impact. 


Pressure. 


.org 


•4g 


F. 

G. - - 

AV. - 


$6% 

52% 
54* 


66% 
30% 

48% 



1 We retain this term for purposes of convenience, there being no other to denote 
stimuli that are perceived with difficulty-. 

54 



SENSA TIONS OF IMP A CT. 5 5 

It is evident from the above that a pressure stimulus has 
a much less intensive effect than one of impact, even if the 
-velocity of the weight applied be very small. If the pres- 
sure were applied more rapidly (between i and 2 sec. was 
the time), the effect upon the dermal end organs would be 
anore marked. But the quicker the increase of pressure 
the more would its effect resemble that of impact. 

Sec. 2. The Threshold of Pain. 

To find the threshold for impact stimuli a wooden upright 
frame was constructed i m. in height. A box containing a 
weight, of lead or brass, could slide in an open groove with- 
out appreciable friction. A scale showed the height in centi- 
metres through which the box fell. The part of the 
stimulus in contact with the skin was of wood and circular in 
shape, the diameter being i cm. The box was allowed to 
fall by the hand, after being raised to the height desired. A 
wax model was made to fit the hand of the observer, so that 
when the hand was once placed under the movable stimulus 
its position could not be changed. The palm of the hand 
was the place of stimulation. By means of this instrument 
the height causing pain was found for different weights. 

The experiment was conducted as follows. The required 
^height having been previously found very roughly, the 
weight was allowed to fall from a height somewhat below 
this point. It was then allowed to fall from a height 5 cm. 
_greater, and this was continued until pain was caused by the 
blow. From two to five experiments were generally made 
before the pain threshold was recorded. As it was found 
that repeated trials made the tissues more sensitive, an inter- 
val of about half a minute elapsed between the experiments. 1 
Pour weights were used, and with two or three exceptions 
but one measurement was made at one sitting for each weight. 
The order in which the heights for the different weights were 
found was the reverse in half of the experiments from that 
which was followed in the other half. Ten experiments for 

1 This precaution was all the more necessary because of the difference in times of 
the appearance of pain and the sensation of impact. This difference was occasionally 
wery marked. 



56 



SENSATIONS FROM PRESSURE AND IMPACT. 



each weight were made by the writer upon himself and five 
upon L., an advanced student of psychology. We give 
below the average values in centimeters of the height neces- 
sary to cause pain for the different weights used. The 
probable errors of the averages are also given, being pre- 
ceded by the sign ±. 



Observer. 


25 g- 


5o g. 


100 g. 


300 g. 


L. 
G. 


32.8=t .5 
69.4^1.1 


i8.6±.4 

34-2 ±.'3 


io.6±.3 
i6.8±.i 


5-4=t .2 


If we multiply the above values for the height by the 
corresponding weights, we obtain the following results : x 




25 g- 


50 2:. 


100 g. 


300 g- 


L. 
G. 


820. ±12. 
1730.^=27. 


930. ±20. 
1710.1+115. 


1060. ±30. 
1680. zb IO. 


930. ±9. 
1620. zb 60 



From this it appears that the product of the weight and 
the height necessary to cause pain is fairly constant. Ex- 
pressing this in the form of an equation we have, 

Wh = k, 
which is the equation of an hyperbola. If for Wh we sub- 
stitute its value, \ m v 2 , we have, 

i m v 2 = k, 
which expresses the relation between the mass and velocity 

necessary to cause pain. If we substitute — for m, we have, 



r2 _ 



2k m. 



This equation expresses the relation of the velocity and the 
mass, considered as factors determining the intensity of the 
stimulus. The equation is that of a parabola. Its meaning 
is that an increase of the square of the velocity has the same 
intensive effect on pain sensations as a corresponding increase 
in the mass. 



1 The probable errors of these results are found by multiplying the original proba- 
ble errors by the weights. 



SENS A TIONS OF IMP A CT. 57 

By taking the average values of the product Wh for the two' 
observers, and comparing these with the average values of the 
pressure threshold for the same area, we find that for L. a 
pressure of about 2300 g. is equivalent to a blow of the same 
mass through a height of 4 mm., and therefore a velocity of 
28 cm. per sec. 1 For G., in like manner, the pressure of 
4500 g. is equivalent to a blow of the same mass having a 
velocity 27 cm. per sec. For velocities less than these 
greater masses would, according to theory, be required for 
impact than for pressure. It is probable, therefore, that the 
equation does not hold for very low velocities. This we 
might naturally expect, since as- the velocity decreases the 
less is the difference between impact and pressure stimu- 
lation. 

Sec. 3. The Analysis of Mass and Velocity in Impact Stimuli; 

When the same weight falls upon the skin from different 
heights, different sensations are aroused. In order to inves- 
tigate the subjective effects of mass and velocity in haptic 
sensations proper, as opposed to those of pain, the writer" 
allowed a weight of 100 g. to fall upon the palm of the ob-" 
server's hand from a height of 5 cm., in the manner already 
described, and then found the approximate height at which 
a weight of 25 g., and the same area, seemed to give rise to' 
a sensation of equal intensity. That height was considered 
the height required, at which, in ten or more trials, about 
half of the observer's judgments were ' heavier ' and half 
1 lighter.' When the experiments were begun, the observers 
were asked to judge which weight seemed heavier or lighter 
rather than which seemed to give the more intense sensation. 
It was, however, evident from the statements made by the 
observers that they judged the intensity of the blow. Some 
spoke of a difference in the quality of the sensations, and two 
said that the weights fell with different velocities. We give 
below the heights determined for different observers at which 
the blow of 25 g. seemed equal to that of 100 g. at 5 cm; 

1 The velocity is readily calculated from the height by the formula, h = — - 



58 



SENSA TIONS FROM PRESSURE AND IMPACT. 



We give also the square roots of the heights, since these 
may be taken to represent the velocities. 



Observer. 


S. F. 


L. F. 


L. 


K. 


P. 


h. 


40 


40 


58 


33 


20 


tin 


6.3 


6.3 


7.6 


5-7 


4-5 



The individual differences are so great that an exact 
inference is impossible. It is, however, evident that in order 
that blows be judged of equal intensity, the height, or the 
square of the velocity, has in general much less effect than 
the weight. For if this were not the case, the average 
height for 25 g., to cause a blow judged equal to that from 
100 g. at 5 cm. would be not far from 20 cm. 1 On the other 
hand the velocity appears to have a relatively greater effect 
than the mass. Otherwise the average values of \/h for 
25 g. would be approximately 8.8 cm. or more. 2 If we assume 
that the above judgments are based upon equality of sensory 
intensity, we may conclude that to cause an intensive effect 
equal to that of the velocity, the mass must increase faster 
than the velocity, but more slowly than the square of the 
velocity. The great individual variations make it probable, 
however, that the process of judgment is somewhat complex. 
Possibly the fact that we are more accustomed to judge 
weights than velocities, may partly account for the difficulty 
observers have in forming a judgment. Then, too, the 
change in sensation due to velocity is of different modality 
from that due to weight. But although we cannot assume 
that a relation is obtained between the intensive effects of 
mass and velocity, this is extremely probable. The com- 
plexity of the processes of comparison is such that great 
individual variations are to be expected ; but to whatever 
extent the judgments be affected by non-peripheral pro- 
cesses, they are doubtless based upon differences in sensory 
intensity. 

1 100 g. X 5 cm. =ae 25 g. X 20 cm. 
1 100 g. X 2.2 cm. = 25 g. X 8.8 cm. 



SENSA TIONS OF IMPACT. 



$9 



Sec. 4. The Discrimination of Mass and Velocity. 



In order to investigate the accuracy of discrimination for 
impact stimuli, an apparatus was used constructed as shown 
in the cut. 



Fig. 7. 




An aluminium bar, AB, movable vertically, was attached 
to a horizontal axis, B, so that it could fall from different 
angular elevations. At the extremity of the bar weights of 
brass or lead could be attached. Metallic upright bars, 
attached to the wooden base, DF, GH, were provided with 
movable clamps, L and M. On these clamps catches were 
fitted by which the experimenter could let the weight and 
bar fall from any desired angular elevation. When a con- 
stant height was used, it was more convenient to let fall the 
weight from an electro-magnet, T. A scale furnished the 
means of adjusting the angular elevations. The stimulus 
was applied to the palm of the left hand, which was placed 
in a wax rest made to fit the hand. The hand was in contact 
with the cylindrical piece, K, projecting from the extremity 
of the weighted aluminium bar when the bar was horizontal. 

Two different sets of experiments were made. In one of 
these the mass applied was variable and the velocity con- 
stant. In the other the mass was constant, the observer 
being required to estimate differences in the intensity of the 
blow from increments in velocity due to height. If K de- 
note the moment of inertia of the falling mass, <o the angular 
velocity, W the weight, v the linear velocity, h the height 



60 SENSA TIONS FROM PRESSURE AND IMPACT. 

through which the centre of gravity falls, and r the distance 
from the axis to the centre of gravity, we have 

|Kft) 2 = Wh 1 

and 

iKr 2 v 2 = Wh. 
Since K r 3 is constant, when the height only is variable, 

v = c /h. 
Hence we may take \/h to represent the velocity when the 
height is varied. This quantity 'is taken as the stimulus 
when the mass is constant, the weight- being allowed to fall 
successively from different heights, and the accuracy of dis- 
crimination being measured by the method of right and 
wrong cases. In order that the judgment might be based 
upon the sensation of impact only, the writer caught the 
lever arm of the weight by the hand the moment after it 
struck the observer's hand. As there was a slight rebound, 
it was thus comparatively easy to eliminate' pressure sensa- 
tions. The values of h for different values of the angular 
elevation of the lever arm, 0, were calculated by the formula 
deduced for the purpose, 

h — r sin (6 -J- a) — /, 
in which a represents the angle betwen the lever arm and the 
line passing from the axis of rotation to the centre of gravity 
of the lever arm and weight, C, and /represents the distance 
from C to the lever arm. The position of C was found by 
experiment. The above formula was roughly verified by 
measurements which, on account of the position of C, were 
too inexact to serve as a basis for calculations. 

In the experiments the results of which are given below 
the standard weight was 50 g. Two standard heights were 
used, 5.4 cm. and 17.5 cm. The increments were for 
height 1.3 cm. and 3.5 cm., and for weight 10 g. The per- 
centage of right answers varied generally between jofi and 
90%. In the tables appended are given the probable errors 

1 For the deduction of this formula, the writer is indebted to Prof. R. S. Wood- 
ward, of Columbia College. If F be the impressed forces, r the lever arm, and 6 the 

d 2 6 
angular elevation, K -^ = Fr = Wr cos 6. Hence, 



K I — &Q = Wr sin 6 = Wh -. I K 
J dt» T 



SENSA TIONS OF IMPACT. 



61 



for the different sets of ioo experiments. 1 The second col- 
umn indicates the nature of the variable stimulus, whether 
•weight, W, or velocity, -/h. When the variable stimulus is 
the weight, the probable error is, of course, in terms of 
•weight. When the variable stimulus is velocity, the prob- 
able error is calculated in terms of \/h. 2 In the sixth col- 

P 

urans are given the values of ~, the average probable error 

divided by the mean of the two stimuli compared. In the 

P 

last columns are the values of ~ for velocity, Rv, divided by 

o 

p 

■~ for weight, Rw. This indicates the ratio of the accuracy 

iOi discrimination for velocity to that for weight. 
H = 5.4 cm. H + AH = 6.7 cm. 



vu = 


2.32 cm. y'H 


+ AH 


= 2 -l 


8 cm. 






Observer. 


Var. S. 


Pi 


P 2 


Av. P. 


I-*- 


Rv 
Rw 


S. F. 
L. F. 


W = 50 g. 
\/h = 2.32 cm. 

W = 50 g. 
\/h = 2.32 cm. 


6-5 
-33 
5-9 

. 12 


8.0 
.25 


7.2 
.29 

5-9 
.12 


.13 = Rw. 
.12 = Rv. 
.11 = Rw. 

.o5==Rv. 


.8 
• 4 



H = 17.5 cm. H + AH = 21. cm. 
j/H = 4.19 cm. -/H + AH = 4.58 cm. 



" 










P 


Rv 


Observer. 


Var. S. 


Pi 


P a 


Av. P. 


s = R. 


Rw 


! S. F. 

: 


W = 50 g. 
\/h = 4.19 cm. 


4.2 
•43 


6.7 

• 43 


5-4 
•43 


. 10 = Rw. 
.10 = Rv. 


1.0 


L. F. 


W = 50 g. 
\/h = 4.19 cm. 


5- 
.23 


3-9 

.27 


4-4 

.25 


.o8 = Rw. 
.o6 = Rv. 


• 7 


L. 


W = 50 g. 
s/h = 4.19 cm. 


6-3 
• 73 


7.7 
.60 


7.0 
,66 


.13 = Rw. 
.15= Rv. 


1.1 



1 See Chap. Ill for method of calculation. The prob. errors are not here cor- 
rected as in Chap. III. 

1 When the weight is varied there is a slight change in the velocity. For a small 
increment of weight, however, this may be neglected, as will be seen from the formula, 
£ Kw 2 = Wh. 



62 SENSA TIONS FROM PRESSURE AND IMPACT. 

In order to compare the accuracy of discrimination for- 
blows with that for pressure stimuli, 400 experiments on S. 
F. and L. F. were made with a weight of 1000 g. and an area 
approximately the same as that used in the impact expert 
ments. We give below the mean of the two probable errors 
obtained for S. F. and for L. F., divided by the mean of the 

P P 

stimuli compared, -~. The values of ■= for 50 g. are also given 

for comparison. These are for the greater height 17.5 cm., 
since, in order to have a logical basis of comparison, it is 
necessary to compare the relative probable errors at inten- 
sities not greatly differing. Weber's law, we have seen, holds 
approximately only for moderately high intensities. This is 
moreover evident from the table since the relative probable 
errors at the two heights are appreciably different. 

P P 

^ for pressure, -^ for impact. 

S. F. ^ 1000 g. T ^ 50 g. x 17-5 cm. 

L. F. T V T V 

From the results given above we may conclude, first that 
there is no marked difference in the accuracy of discrimina- 
tion for pressure and for impact, and second, that the dis- 
crimination for velocity tends to be more accurate than that 
of weight. If, however, instead of calculating the probable 
errors for the square root of the height, we had calculated 
them for the height, which represents the energy of the blow-, 
we should have found that the discrimination was better for 
the mass than the height. This difference in the discrimina- 
tion for mass and velocity may be due to processes of percep- 
tion or to actual differences in the intensive effects of mass 
and velocity. If we assume that the latter explanation is the 
true one, we can say that in order to produce equal sensory 
effects the relative increments of mass and velocity are related 
as expressed by the equation, 

Av Am 

v m 

Rv . 

in which k is a constant, having: the same value as yt - in the 



SENSA TWNS OF IMP A CT. 63, 

tables. If this equation hold, whatever be the values of Am 

and Av, we have, 

dv , dm 

v m 

whence, by integration, 

log. C + log. v = k log. m, 

in which log. C may be taken as the constant of integration.. 
From this we have, 

C v = m k 
or, 

v = C r m k . 

Rv 

Substituting for k the average of the values of ■= — , 

.Kw 

v = C'mA. 

That is, the velocity increases as m-rV. As it is more con- 
venient to take the mass as the most direct factor in the in- 
tensive effect of the stimulus, the above relation may be 
expressed, 

m = C'V- 3 

We may, therefore, write as the intensive stimulus in im- 
pact, S, 

S = mv 1 - 3 

The quantity k is so difficult to determine, whether or not 
it be variable for individuals, that the above expression is 
only approximate. It is, however, clear that the stimulus is 
to be judged a quantity varying between the momentum mv, 
and the kinetic energy, mv 2 . In other words the mass 
has greater intensive effect than the energy due to the veloc- 
ity, but less effect than the velocity. 

It is possible that the results obtained are dependent 
entirely on the processes of comparison and judgment. The 
conclusion at which we arrived, assuming this not to be the 
explanation, is the same as that which we reached in the ex- 
periments on the direct comparison of the intensive effects of 
mass and velocity. It seems, therefore, preferable to con- 
sider the complex central process involved as causally 
related only to the great individual variations. It is, never- 
theless, not to be assumed that these variations are entirely 



,64 SENS A TIONS FROM PRESSURE AND IMPACT. 

f of central origin. They may be due to differences in the 
sensitiveness of the dermal nerves to impact stimuli. The 
problem becomes still more complex in view of the fact that, 
; as we have found, the pain threshold is determined, approxi- 
mately at least, by the kinetic energy of the blow. This 
might be explained teleologically in that the injury done to 
the organism would tend to vary as the energy of the 
blow. If, as we think probable, dermal pain is a distinct 
-sensation, with perhaps a distinct anatomical and physiolo- 
gical basis, it is not surprising that its stimulus should be 
^different from that for impact sensations proper. 



CHAPTER VI. 

The Area of Stimulation. 

Sec. i. The Area of Stimulation and Judgments of the Inten- 
sity of the Stimulus. 

It is a common experience that a needle or other stimulus 
acting on a small dermal area will cause pain, when the same 
pressure applied to a large area will not. The intensity of 
haptic sensations appears, therefore, inversely related to the 
area of stimulation. For the study of this problem different 
methods were used, the first of which will now be described. 

Boxes constructed as described in Chapter III, Sec. 2, 
were applied successively to the volar surface of the left 
hand, and the observer was required to say which seemed 
the heavier. The area of one of the bases, which were 
circular, was 8 sq. cm., that of the other was .12 sq. cm. 
approximately, that is -fa of the larger area. For conven- 
ience we shall speak of the larger area as A, and that of the 
smaller as a. Two sets of experiments by the method of 
right and wrong cases were carried on simultaneously. In 
one set an increment, which we shall call A lf was added to 
the box A, weighted to 200 g., so that a, weighted to 200 g., 
was generally judged the lighter. In this set A was always 
the first to be applied. In the other set a different increment 
(A 2 ) was added to A, such that A4-A 2 was generally judged 
lighter than a. In this series a was always the first to 
be given. In this way the observer could not be influenced 
by the association of one area with an apparently greater 
intensity. 

The method of calculating the overestimation of the in- 
tensity of a is as follows. 

Let C.E. be the constant error due to overestimation of 
the second of two stimuli, P.E. the probable error, T h and 

65 



66 SENSA TIONS FROM PRESSURE AND IMPACT. 

T t the values of the probability integral corresponding to the 
percentages the second stimulus is judged heavier and 
lighter, and N, the required constant overestimation of the 
stimulus acting on the smaller area. Then for the series 
A-\-A x as first, and a as second stimulus, from the formula, 

A 

= T 

P.E. h ' 



we have, 5-^ = T h 



C.E. + N— A, 
P.E. 



whence, N=T h P,E.+A 1 — C.E. 

For the series a as first, and A-\-A 2 as second stimulus, we 
have, 

N— C.E.— A 2 

P.E. *' 

whence, N=T, P. E+A 2 -f C. E. 

The values of P.E. and C.E. having been found by ex- 
periments carried on simultaneously with these, the values 
of N were calculated from the above equations. With W., 
an advanced student of psychology, 400 experiments were 
made, and the values of N for each set of 100 were as 
follows : 

J* 
S 

i/3 

The overestimation of the weight applied to about g 1 ^ of 
the larger area was, therefore, approximately ^ of the stimu- 
lus. Experiments were also made by another method, and on 
a number of observers. The method of right and wrong cases 
was used, but the relations of the stimuli were different. 
The first stimulus was constant, and had the smaller area. 
The second stimulus was part of the time A+A lt and part of 
the time A-\-A 2 , the values of A 1 and A 2 being such that 
A-\-A x was judged heavier and A-±A 2 lighter than a, the con- 
stant first stimulus. By this method from twenty to fifty 
experiments were made on W., N. F., L. S., and McW., all 
being subjects in the experiments on discrimination of 
weights already described. Not enough experiments were 



Observer, W. 


N, 


. N, 


N 5 


N, 


Av.N 


Stimulus, 200 g., 


65 


68 


75 


69 


69 



THE AREA OF STIMULA TION. 67 

made to base a calculation upon them, but enough to esti- 
mate roughly the overestimation. The results for W. were 
corroborative of those already obtained, both for 100 g. and 
200 g. L. S. and McW. showed an overestimation at 500 g. 
of about -|- the stimulus, closely corresponding to that of W. 
N. F. showed, however, an appreciable tendency to under- 
estimate the weight of a at 100 g. and also at 200 g. 

By a third method the increment added to a weight with 
area A pressing on the hand in order to make it appear equal 
to the same weight lifted was compared to the increment 
which had to be added when the area was a instead of A. 
Below are the values of the increments obtained for a 200 g. 
weight, each based upon five or more experiments. The 
observers were, of course, ignorant of the purpose of the 
experiment, as well as of the magnitude of the increments. 

P. K. L.F. S.F. 

A. 37 o 150 148 

a. 00 o 140 

In only two of the four observers does this overestimation 
due to the area appear very marked in these experiments. 
From this, and from the fact that by a different method there 
was not only no overestimation found for N. F., but even 
the reverse, we may conclude that this constant tendency is 
by no means universal. 

The fact that individual variations are such that we can- 
not infer a relation between the area and the intensity of 
stimulation does not prove that such a relation does not 
exist. An observer may unconsciously allow for this over- 
estimation in his judgment, though this was certainly not 
the case with N. F., since this observer supposed the larger 
area would seem heavier. It is difficult, moreover, to 
explain in this way the results obtained by the last method. 
But in the direct comparison of weights of different areas, 
great difficulty is experienced by some observers in forming 
a judgment. The sensations seem heterogeneous and there- 
fore incomparable. It is only by abstraction that a judgment 
of intensity is possible ; and in this process it is but natural 
that individuals should differ greatly. 



68 



SENSA TIONS FROM PRESSURE AND IMPACT. 



Sec. 2. The Tactile Threshold. 

If the intensity of haptic sensations is related to the area 
of stimulation, we should expect the tactile threshold to vary 
with the area. For the purpose of investigating this prob- 
lem, the writer cut circular pieces of card board about 3.5 
mm. and 10.7 mm. in diameter, their areas being, therefore, 
approximately in the ratio 1 : 9. The weights of the cards 
were about .01 g. and .05 g. ; but this may be neglected, 
since only at the moment of application of the weight do 
pressure stimuli of low intensity have any sensory effect. 
When one or both of these cards had been placed on the 
palm of the hand of the observer, who was blindfolded, the 
pressure necessary to affect consciousness was found by the 
apparatus and methods described in Chapter II. The same 
corrections are also made. Ten experiments for each area 
were made on L. F. by the writer, and as many on the writer 
by S.F., who was carefully instructed as to the precautions 
necessary. A third set of experiments was made in which 
no card was used, the pressure being exerted directly upon 
the skin by the vertically projecting bristle of the instru- 
ment. The diameter of the bristle being about .4 mm. the 
area applied was about 1.2 mm. Below are the results in 
grams for each group of ten experiments. 



Area. 


Av. 


S. F. 
Max. 


Min. 


Av. 


H. G. 

Max. 


Min. 


1 mm. 
10 mm. 
90 mm. 


.2 

•9 
1.9 


•5 

1.; 

2.7 


.1 

•3 
1. 


•5 
1.4 
1.6 


1. 

3-2 
2.5 


.2 

•3 
•4 



It appears from this that the tactile threshold varies with 
the area of stimulation, but that it increases much more 
slowly than in direct proportion. From what we have already 
said regarding the possibility of regarding the threshold as 
a definite quantity more exact results could hardly be ex- 
pected. Strictly speaking we are not justified in using the 
term threshold, but it is convenient to do so, if we bear in 
mind that no absolute quantity is measured, but only the 
relative sensory effect of stimuli acting on different areas. 



THE AREA OF STIMULA TION. 6$ 

Sec. 3. The Threshold of Pain. 

In order to investigate this relation with accuracy, 
wooden cones of hard wood were cut across vertically by a 
lathe at three points so determined by calculation that the 
diameters of the sections would be approximately 6.18 mm., 
10.70 mm., and 18.54 mm. A still smaller circular base, 
about 3.56 mm. in diameter, was made by rotating a wooden 
cone cut by hand over sand paper until the diameter required 
was obtained. In this way areas were obtained of approxi- 
mately 10, 30, 90, and 270 sq. mm. The diameters of the 
two smaller bases were measured a number of times on the 
dividing engine. The averages of five readings were 6.21 
cm. and 3.58 cm., which shows that the areas are sufficiently 
accurate. In applying the pressure the algometer already 
described was used. The pressure was exerted upon the 
desired area by fitting the upper part of the wooden piece, the 
base of which had the area in question, into another wooden 
piece. Into this in turn could be fitted the projecting cap of 
the algometer. The rate of increase of the pressure was 
kept as constant as possible, and this was as great as was 
consistent with taking the readings accurately. The error 
due to the increase of pressure between the appearance of 
the pain and the taking of the reading is corrected as in 
Chapter II. It will, therefore, not affect the results. The 
place of stimulation was the palm of the hand. With F. the 
right hand was used, but the left hand was used in experi- 
ments on G. But four experiments were made on one day, 
one for each area. In half of the experiments the order in 
which the different areas were used was the reverse of that 
which was followed in the other half. Though the experi- 
ments made by the writer on himself were purposely extended 
over several weeks, a gradual decrease of sensitiveness to 
dermal pain was observed. This is not so noticeable in the 
results found for S. F. The averages, with their probable 
errors, 1 are given below, for each set of five experiments. 
The figures indicate kilograms. 

1 As the quantity determined increases appreciably for G. , the use of the probable 
error is not justified, and it is not given. 



7o 



SENSA TIONS FROM PRESSURE AND IMPACT. 



Observer. 


Group. 


Area. 


. i cm. 


.3 cm. 


.9 cm. 


2.7 cm. 


S. F. 


ist five. 
2nd five. 


i-4i.o 

1.9=1=. 1 


2.7. i=fc 
2. 7. =1=1 


3. ±.1 
3.4=1=. 1 


4.5=fc.2 
4.8±.2 


G. 


ist five. 
2nd five. 


1. 

1-3 


2.6 

3-1 


4.6 
6.8 


7-3 
10. 


Av. 




1.4 


2.8 


4.4 


6.6 



These results are represented graphically in the accom- 
panying-curves. 

FIGURE 8. 



Thtens- 




Area. 



to $0 



As the curves obtained differ somewhat, it is impossible 
to express the relations by a simple expression. They ap- 
proximately are logarithmic curves, but for the largest area 
the increase of intensity is too great. As the stimuli are 
in geometrical progression, the logarithmic relation requires 
an arithmetical increase of the area. We may, therefore, 
test the results by finding the differences between the thresh- 
old at the different areas. These differences are as follows : 

10 and 30 mm. 30 and 90 mm. 90 and 270 mm. 



S. F. 


i-3 


S. F. 


.8 


G. 


1.6 


G. 


1.8 


Av. 


1-3 



i-5 

1.4 

2.7 

3-2 
2.2 



The v increments appear to increase with the area, whereas 
an arithmetical progression requires that they be constant. 



THE AREA OF STIMULATION. 7 1 

But as will be seen by inspection of the above figures, the 
increase is within the limit of individual and other variations. 

Sec. 4. Theoretic hiterpretation of Experiments on the Intensive 
Effect of the Area. 

We have by three entirely different methods investigated 
the intensive effect of the area of stimulation. By each one 
of these methods we have arrived at the same result, that 
the intensity of pressure sensations is inversely related to 
the area of stimulation. We have seen that the intensity 
causing pain is approximately proportional to the logarithm 
of the area. Hence, as the intensity of the stimulus increases, 
its effect is the same as that from the decrease of the corre- 
sponding logarithm of the area. The experiments on the 
tactile threshold and on judgments of intensity, though not 
admitting of such an interpretation, nevertheless seem to 
show that the intensity threshold increases much more slowly 
than the area. Hence we may write as an approximate 
expression of the relation between the intensity and the area 
of the stimulus which must exist in order that equal subjec- 
tive intensive effects be produced, 

1= -*- 

log A 

If we could assume Fechner's law we could substitute the 
value of I in the equation, 

S = K, log I, 

in which S denotes intensity of sensation, and obtain, 

S = K. logLJLr-V 

1 5 Vlog A/ 

That is, the intensity of the sensation increases as the 
logarithm of the reciprocal of the logarithm of the area 
multiplied by a constant. If, as Hering and some others 
hold, S is directly related to I, the relation between S and 
A would be an inverse logarithmic one. If, as the majority 
of psycho-physicists believe, S increases much more slowly 
than I, even though not in logarithmic proportion, it would 
increase correspondingly more slowly than the reciprocal of 
the logarithm of the area. The inverse relation here exist- 



72 SENSA TIONS FROM PRESSURE AND IMPACT. 

ing is contrary to what we might expect by the analogy of 
other senses. In the case of temperature sensations Weber 
showed that the intensity increased with the area. 1 Miiiler— 
Lyer found that the least noticeable difference for visual 
stimuli increased with the area of stimulation in about the 
same proportion as when the intensity was variable and the 
area constant. 2 With pressure stimuli the conditions are 
apparently the same ; the larger the area the greater the 
number of nerve fibres stimulated. 3 If the stimulus were 
the physical pressure exerted, the intensity would, we think, 
increase with the area. For not only are more nerves acted 
on by larger areas, but the pressure increases in direct pro- 
portion to the area, provided the force applied be constant. 
As the exact reverse effect is produced upon the sensory 
end organs, the stimulus can not be considered mere pres- 
sure, but rather as work done upon the skin and subcutane- 
ous tissues. 

In sensations of impact the stimulus is, as we have seen, 
the energy of the moving mass or a quantity more approach- 
ing to the momentum. 4 In the case of impact stimuli, there- 
fore, we should not expect the intensity of the sensation to in- 
crease, but rather to diminish with the area. For the greater 
the area the less the energy or momentum transferred to the 
dermal tissues within a given area. When no impact, but 
only pressure, is exerted, then the stimulus is the work 
expended in overcoming the resistance of the skin. The 
work done is independent of the area of stimulation, as it de- 
pends upon the impressed forces. Consequently, the greater 
the area the less is the work done at any one point in the 
region affected by the pressure ; in other words, the less 
the intensity of stimulation. If, moreover, the function of 
the touch corpuscles be protective, as some suppose, the 
stimulus will meet with greater resistance, the greater the 
area upon which it acts. 

1 Weber, op. cit., 553; also Dessoir, op. cit., 297. 
2 Muller-Lyer, Archiv fur Anat. und Physiol., 1889, Supp. Bd. 
3 Funke even states that the intensity increases with the area. Op. cit., 331. 
*The movement theory of haptic stimulation was, we believe, first advanced by 
Lotze, Med. Psychologie, 198. 



THE AREA OF STIMULA TION. 



73 



This leads us to the consideration of the peculiar phe- 
nomena of dermal pressure from liquid or gaseous bodies. 
The atmosphere exerts a pressure upon the body of 1.03 
k. per sq. centimeter, but has no effect upon conscious- 
ness. When the hand is placed in a fluid, even of consider- 
able density, no pressure is felt except at the surface. These 
phenomena are intelligible, when we consider that the pro- 
cess of haptic stimulation involves a transference of energy. 
The element of time is of not a little importance, but will be 
considered later. The ring effect observed when the hand 
is plunged in mercury has its counterpart in the relatively 
great intensity of pressure sensations from solid stimuli in 
the region of the perimeter of the surface applied. A kilo- 
gram weight placed on the hand will be felt most distinctly 
at the edge. That the skin is more affected in this region is 
shown by the dark red line from vaso-motor disturbance 
that here appears when the stimulus is removed. It is not 
necessary, therefore, to explain the phenomena by such 
hypotheses as that of Meissner, who held that the process of 
pressure stimulation was an oscillatory action in the tactile 
corpuscles. 1 

Sec. 5. The Area of Stimulation and the Discrimination of 
Intensity. 

In the chapter on the accuracy of discrimination for 
different intensities, two areas were used, 8 cm. and -g 8 ^ cm., 
approximately- In addition to the experiments there de- 
scribed, 1000 experiments were made on W. In 500 of 
these the larger area was used, and in the other 500 the 
smaller area. In the following table will be found the prob- 
able and constant errors based upon each set of 100 experi- 
ments. 

Stimulus, 200 g. 



Area. 


Pi 


P 2 


Ps 


P 4 


Ps 


Av. P. 


Ci 


C2 


c 3 


c 4 


c 5 


Av.C. 


8 cm. 


37 


19. 


22. 


20. 


14. 


22. 


i5 


10 


i5 


9 


5 


11 


<nr cm - 


33 


56 


10. 


14 


16 


25 


3 2 


8 


9 


3 


12 


13 



1 Meissner, Zeit. fur Rat. Med., 3 te R., VII. Cf. Funke, op. cit., 328, for a 
criticism of Meissner' s theory. 



74 



SENSATIONS FROM PRESSURE AND IMPACT. 



From these results it is evident that the accuracy of dis- 
crimination of this observer was not on the whole appre- 
ciably altered by the variation of the area. The same might 
be said of the constant error. The variation of the probable 
error for the smaller area is, however, so great that in spite of 
the large number of experiments, the results do not admit of 
an exact interpretation. By comparing the average values of 
P 

— for the observers S. F., J. S. and L. S., on whom experi- 
ments were made for both areas, we obtain somewhat more 
satisfactory results. By referring to the tables, Chap. Ill, 
Sec. 3, we see that although N. F.'s probable errors are 
very variable, especially for the smaller area, those of L. S. 
for both areas are fairly constant. The following table 

p 

gives the average values of — ' the probable error divided by 

the stimulus, for all intensities used. 



Area. 


Average values of — • 


N.F. 


J. S. 


L. S. 


W. 


8 cm. 

A cm - 


•13 
.18 


.1 1 
.12 


.10 
. 10 


.1 1 
•13 



Although W. and N. F. appear to judge stimuli of the 
larger area more accurately, there is no appreciable difference 
for J. S. and L. S., the most constant of the four observers. 



Sec. 6. The hitensity of Stimulation and the Discrimination 
of Areas. 

It was not our purpose to enter into a discussion of the 
problem of tactile space perception. But having found that 
the discrimination of intensity was not uniformly affected 
by the area of stimulation, the question suggested itself 
whether the converse was true. For the purpose of finding 
if this were so, weights were used of 200 g. and 800 g. Two 



THE AREA OF STIMULA TION. 



75 



standard areas were used, being approximately 32 mm. and 
1 1.3 mm. in diameter, and therefore 800 mm. and 100 mm. 
in area. The bases of the boxes applied were covered with 
stiff paper cut so as to be circular in shape. We were not 
investigating the absolute accuracy of discrimination of 
areas, nor yet the relation of this to the magnitude of the 
area; consequently any errors due to the method of obtain- 
ing the different areas may be neglected. The probable and 
constant errors given in the tables are, of course, in millime- 
ters. They were obtained, as in other experiments, by the 
method of right and wrong cases, from the percentage of 
right answers in a hundred experiments. In these experi- 
ments the area is considered the stimulus, S, and the incre- 
ment A, is the difference between the area of the standard, 
100 or 800 mm., and that of the area to be compared. The 
magnitude of the increment is obtained by the equation, 

A = 7T (r 2 — r, 2 ,) = 7T (r + r„) (r — r^), 

in which r and r, are the radii of the bases. The first of the 
two tables gives the results for three observers, the smaller 
area being used. The second table gives corresponding 
results for the larger area. But 100 experiments were made 
upon N. F. and W. for each of the probable errors calcu- 
lated. The probable errors for L. S., however, are each 
calculated from the results of 300 experiments. 

Area, 100 mm. 





Probable Error. 




Weight. 


L. S. 


N. F. 


W. 


Av. 


200 g. 
800 g. 


43 
3I 1 


40 


21 

47 


3i 
39 




Ar 


ea, 800 mm. 




200 g. 
800 g. 


73 
9I 1 


47 
70 


41 
69 


53 
73 



A weight of iooo g. , instead of 800 g. , was used in experiments on L. S. 



y6 SENSATIONS FROM PRESSURE AND IMPACT. 

The figures above given show that the discrimination for 
areas is not as accurate for the high intensity, the probable 
errors for 800 g. being in four cases out of five much greater 
than for 200 g. The one exception appears in the experi- 
ments on L. S. for the smaller area. In conducting these 
experiments, however, it was found that the accuracy of 
discrimination for 800 g. increased to such an extent from 
practice that the variable area had to be changed in order 
that the increment might not be too great for accurate cal- 
culation of the probable error. In the first few experiments 
made, then, the accuracy of discrimination was undoubtedly 
much less for 800 g. than for 200 g. There was, however,, 
no appreciable improvement from practice after thirty or 
forty experiments. The apparent exception, therefore, par- 
tially confirms the results obtained for the other observers. 

If we compare the second table with the first, we note 
that the probable error for the larger area, although appre- 
ciably greater, does not increase in proportion to the 
areas. It is possible that in these experiments what is really 
discriminated is the linear relation, that is, the relative 
diameters of the circles. This is, however, not probable ; 
for the difference felt seems to be a qualitative difference in, 
the sensations from which that of space is inferred. The 
change in sensation corresponding to change in the area of 
stimulation might, indeed, be supposed to be merely a quan- 
titative change in extensity. But the great difficulty observ- 
ers have of comparing intensities of different areas confirms 
the results of the writer's introspection, that this change in 
sensation is not primarily a spatial change. 



CHAPTER VII. 

The Time of Stimulation. 

Sec. I. The Intensity of Haptic Sensations in Relation to the 
Time : Low Intensities. 

The intensity of visual and temperature sensations is 
clearly related to the time of stimulation. But if a weight 
of low intensity, and of not too small an area, be applied to 
the skin, the resulting sensation will continue but a few sec- 
onds, and will not increase, as might be expected, with the 
time of application. It is largely on this principle that the 
phenomena of gaseous and liquid pressure may be explained. 
The pressure of the atmosphere is fairly constant, and is, 
therefore, not perceived. Meissner observed that melted 
wax allowed to harden on the hand had no sensory effect, 
although his explanation is different from that here given. 
When the hand is plunged in mercury and held in the same 
position, the pressure remains constant, and it is only when 
the hand is moved that the pressure sensation is distinct. 1 
Hall and Motora found, contrary to what we might expect, 
that the discrimination of gradual pressure change was best 
for the slowest rate of change of stimulus that was used, 
2^j of the stimulus per second. 2 In these experiments the 
observer had first to decide whether the stimulus was increas- 
ing or decreasing ; and it is probable that, as suggested by 
the writers, the cause of the decrease in the accuracy of dis- 
crimination was the distracting effect of sudden changes 
upon the attention, and consequently upon the accuracy of 
perception. 

We intended to make experiments on judgments of in- 
tensity in relation to the time of stimulation, but the appa- 

1 Cf. Meissner, op. cit. 

* Hall and Motora, Am. Journ. Psy., I, 87. 

77 



7 8 SENSA TIONS FROM PRESSURE AND IMPACT. 

rent impossibility of eliminating the error arising from 
memory of the standard stimulus led us to confine ourselves 
to qualitative observations. We did, however, make experi- 
ments on the intensive effect of the time for stimuli of such 
low intensity as to be perceived with difficulty. The instru- 
ment used was that already described, by which pressure 
was exerted by the hand of the experimenter. 1 There was 
no means of regulating the rate of application of the pres- 
sure except the judgment of the experimenter, and the 
results must therefore be considered as inexact. The ex- 
perimenter practised himself in increasing the pressure at 
such a rate that it took 8-10 sec. to reach a pressure of -4g. 
In like manner a time of 1-2 sec. was obtained. The third 
time of application was the shortest, i— \ sec, the increase 
being as rapid as was consistent with accuracy. The rates 
of increase were, therefore, .05-. 04 g., .4-. 2 g. and 2.3-1.6 g. 
per sec. The maximum pressure, -4g., was, of course, kept 
fairly constant. Fifty experiments were made for each rate 
by the writer on S. F., and as many by S. F. on the writer. 
In the tables below are the percentages of times the stimu- 
lus .4 g. was perceived at the different rates of increase. 

•05 — -o4g. 4-.2 g. 2.3--1.6 g. 
per sec. 
S. F. - - \o% 
G. - - 2% 

Av. - - 6% 

From these results it is evident that the sensory effect of 
pressure stimuli increases with the rate of application. This 
is what we should expect on the assumption that the inten- 
sity of pressure sensations decreases rapidly with the time 
of application. 

As for the theoretic interpretation of these results, we 
judge them corroborative of the movement theory of dermal 
stimulation. The stimulus is not to be considered mere 
pressure, but the energy expended upon the dermal tissues. 
From this point of view we are not justified in identifying 
the time of application of a pressure stimulus with the time 

1 See Chap. II, Sec. 3. 



per sec. 


per sec 


34/< 


82% 


30% 


S2% 


32% 


%2% 



THE TIME OF STIMULATION. 79 

of actual stimulation. If a vibrating tuning-fork of suffi- 
cient amplitude to cause a distinct sensation be placed in 
contact with the skin, there is continued intermittent stimu- 
lation, and the sensation does not decrease as when a pres- 
sure stimulus is applied. The intermittent process of stimu- 
lation by the tuning-fork is similar to that of visual and 
auditory stimulation, for the physical stimuli are successive 
transformations of energy. 

The time phenomena of pressure stimulation may also be 
brought under the general law that it is not static condi- 
tions, but changes in the environment that give rise to the 
'nervous shock' of Spencerian psychology. It is such 
conditions of the environment that the organism needs to 
perceive in order to coordinate its motor activities for pur- 
poses of self-preservation and reproduction. The cataplec- 
tic shock so frequently experienced when one is unexpect- 
edly addressed, shows how sensitive the central nervous 
system is to sudden peripheral changes. But we need not 
depend only upon observation for proofs of this principle. 
It is well known that motion on the skin may be perceived 
within the circumference of Weber's sensor circles; and 
Hall and Donaldson found that the perception of motion is 
independent of direction, and is clearest immediately after 
the motion begins. 1 In fact, the time phenomena of dermal 
sensations point clearly to the difference theory of sensation, 
according to which change in the objective environment and 
in the subjective mind is the sine qua non of sensation. 2 The 
psychological generalization has, moreover, a demonstrable 
physiological basis. Only on making or breaking an elec- 
tric circuit is a motor nerve stimulated. More closely bear- 
ing on our problem are the experiments of Fontana, who 
found that pressure could be applied so gradually as to kill a 
motor nerve without inducing muscular contraction. Simi- 
lar results have been obtained for temperature stimuli. 3 



1 Hall and Donaldson, Mind, X, 556. 

2 Cf. Hoffding, op. cit., 138, 141 ; Dessoir, op. cit., 188 

3 Heinzmann, Archiv. fur gesammte Physiol., VI, 222. 



80 SENSA TJONS FROM PRESSURE AND IMPACT. 

Sec. 2. HigJi Inte?isities. 



"S 



When stimuli beyond a certain intensity are applied, the 
phenomena are quite different. If a kilogram weight be 
placed on the hand, the intensity of the sensation seems 
gradually to increase and to pass into pain. Miiller observed 
that a sensation of pricking and of having a limb ' asleep ' 
could be caused by long-continued pressure stimulation. 1 
Similar observations on temperature stimuli were made by 
Weber. Thus it appears that heterogeneous sensations 
may be caused by variations in the time of application of 
dermal stimuli. 

For the purpose of investigating the relation between the 
time of pressure causing pain and the intensive pain thres- 
hold, weights of different magnitudes were placed in a bal- 
ance pan so as to act on a constant area of the palm of the 
hand, and the time was noted which elapsed before the ap- 
pearance of pain. To the under side of the balance pan a 
wooden piece was fastened, the circular end of which, 1.5 mm. 
in diameter, came in contact with the palm of the hand. 
The longer times were recorded by a watch, and the shorter 
times by the Hipp chronoscope, a Morse key being so placed 
that the observer could close the circuit as he applied the 
weight without appreciable error. The place of stimulation 
was varied within a radius of about 1 cm. ; otherwise there 
would have been danger of alterations in the condition of the 
skin at the place of stimulation as the experiments pro- 
gressed. Ten experiments were made for each weight on 
two observers, S. F. and the writer. 2 But one experiment 
for a given weight was made on any one day, and not more 
than three or four times a week were these experiments 
made. The order of half of the experiments was the reverse 
of that of the other half. The figures below indicate the 
time in seconds for the various stimuli to cause pain. Only 
the averages are given, together with their probable errors. 



1 Quoted by Weber, op. cit. 

1 Experiments were begun on another observer, but were not completed. It was 
evident, however, that results would have been obtained similar to those obtained for 
G. and S. F. 



THE TIME OF STIMULATION. 



81 



Observer. 


100 g. 


200 g. 


300 g. 


500 g. 


S. F. . . 
G. . 


294 rb 3°- 
167 db 17. 


37± 3.6 
34± 2.7 


8. d= .9 
12 ± 1.5 


3-3 ± .2 
6. ± .06 



The results shown above are represented graphically in 
the accompanying curves. 

Figure 9, 
Time 




(00 



2.00 



500 Intensity 



The experiments prove beyond question that the pain 
threshold is functionally related to the time as well as the 
intensity of stimulation. The results obtained are . not 
sufficiently exact to admit of an analytical expression. It 
appears that the time curve approaches O as its limit for 
high intensities, and that for low intensities it either increases 
indefinitely or approaches as its limit an asympotic line 
parallel to the axis T. That the ascending branch does 
approach a limit is evident from introspective observation. 
Weights of low intensities soon cease to be perceptible, and 
never become painful. Thus the clothing we wear exerts 
continual pressure, but is never painful. The curves ob- 
tained may be said, therefore, to resemble rectangular hyper- 
bolas. If the relation between the time and intensity caus- 
ing pain could be thus represented, it would be expressed 
analytically by the equation, 

(I_h) T = k, 



82 SENSA TIONS FROM PRESSURE AND IMPACT. 

in which h is a constant, being- the intensity below which 
stimuli are never painful. To obtain the relation between 
the time and intensity having equal intensive effects as the 
sensation increases in intensity, we can substitute in the 
above equation the reciprocal of T, since the intensive effect 
would of course decrease as the threshold increases. We 
then have, 

T I — h 

~k E" 

From this equation, that of a straight line, we see that as 
regards their intensive effect on pain sensations, the inten- 
sity and time of the stimulus increase in direct proportion. 

A striking feature of the above experiments is the great 
variation in the time before the pain appears. This is, 
however, only partially a true variation. It is generally 
difficult to decide, especially for low intensities, when the 
stimulus becomes painful. This is quite the contrary of 
what we found to be the case when the intensive threshold 
was being determined. There is, however, no constancy 
even in the manner of variation. At times for the ioo g. 
stimulus the pain would come very suddenly, only to cease 
and reappear, but generally the appearance of pain was very 
gradual. The sensation seemed to increase in intensity 
before the pain was distinctly felt. In the experiments on 
ioo g. a latent period seemed to elapse before any appre- 
ciable increase in intensity began. This latent period for 
S. F. seemed to be on the average about half of the total 
time. The two observers disagreed as to whether there was 
any appreciable decrease in intensity before the increase 
began. 

We are not justified in assuming that the relation be- 
tween the time of pressure and the intensity of pain holds 
also for pressure sensations. The gradual appearance of 
the dermal pain, preceded by an apparent increase of pres- 
sure intensity, undoubtedly points to such a conclusion. 
But the results admit of another interpretation. It is quite 
possible that the mind confuses the incipient pain with the 
pressure sensation. As we know dermal pain to be related 
to the intensity of the stimulus, and as we are not accus^ 



THE TIME OF STIMULATION. 83 

tomed to think so much of the time as a factor, it is but 
natural that we should judge the change in sensation to be 
due to more intense stimulation. We should then consider 
this change an intensive change, until the painful element 
became so clear as to be distinct in consciousness. That it 
is difficult to distinguish heterogeneous sensations of very 
low intensity is shown by the experiments of Wunderli. 1 

Moreover, our experiments are, we think, corroborative 
of the theory that sensations of pain and pressure are utterly 
disparate. For, otherwise, how could we explain the fact 
that the intensity of pain increases with the time, whereas 
the intensity of pressure sensations, at least for low intensi- 
ties, decreases rapidly with the time ? Equally difficult to 
account for on the algedonic tone theory is the continuation 
of the pain after the cessation of stimulation, which was 
very marked for 100 g. 

But if pain be a distinct sensation, with a distinct physi- 
cal basis, the results are quite intelligible. From this point 
of view, we can understand how pressure without appre- 
ciable transformation of energy can be considered a stimu- 
lus to pain. Unlike haptic sensations proper, dermal pain 
furnishes the sensory data for perceptions, not of the object- 
ive environment, but of the subjective self; and may, there- 
fore, be induced by any stimulus of sufficient intensity. 
This view finds further support in teleological considera- 
tions. If pain exist for the purpose of warning the higher 
centres of injury done to the tissues, the intensity of pain 
would, we should expect, be related to the time of pres- 
sure ; for the longer the time of pressure the greater the 
resultant injury to the tissues. 

^eeCh. I, Sec. 2. 



SUMMARY. 

We shall now present a brief summary of the more im- 
portant results of the investigations described in the preced- 
ing pages. 

A. — Experimental. 

i. Hot and cold stimuli are overestimated for low inten- 
sities, but not for high intensities. 

2. The estimate of the intensity of haptic stimuli in- 

creases for low intensities much more slowly 
than the stimulus ; but as the stimulus approaches 
the pain threshold, the estimate of intensity in- 
creases much faster. 

3. The intensive pain threshold, for pressure acting on 

.5 cm. of the hand, varies greatly with individ- 
uals, the average being 5400 g. Age and sex 
appear to have less effect than individual differ- 
ences. 

4. The average value of the least perceptible pressure 

acting on an area of .9 cm., the rate of increase 
being about .3 g. per sec, was 1.9 g. for S. F. 
and 2.6 g. for G. The intensive range of haptic 
sensations for these observers, as based upon 
these measurements, was about 1700. 

5. Weber's law holds approximately for weights greater 

than 100 to 500 g. For low intensities the prob- 
able error increases much more slowly than the 
stimulus. 

6. The average value of the ratio of the probable error 

to the stimulus for stimuli of from 100 g. to 3000 
g. is f 
84 



SUMMARY. 85 

7. The constant error is frequently very great for pres- 

sure stimuli. It increases with the stimulus, but 
the relation is complex, and is subject to great 
individual variations. Some observers have no 
constant error except for stimuli of very great 
intensity. The constant error is more variable 
than the probable error. Its magnitude seems 
inversely related to the accuracy of discrimina- 
tion. A great constant error for pressure does 
not necessitate one for lifted weights. 

8. The degree of confidence in the perception of inten- 

sive differences varies greatly for individuals, the 
proportion of wrong judgments of which observ- 
ers were confident ranging from \ to 5V The 
probability of correctness when confident was 
for most observers from .8 to .9. There is no 
relation between either of these quantities and 
the accuracy of discrimination. The percentage 
of correct guesses varied from 52% to 70%, the 
average being 59%. 

9. The accuracy of discrimination for weights of 100 g. 

or more is, on the average, not appreciably differ- 
ent for the palm of the hand, the back of the 
hand and the volar surface of the index finger. 
For 5-7 g. the accuracy of discrimination, as 
found from one observer, for the palm of the 
hand and the back of the forearm, is less than for 
the index finger, but improves greatly by prac- 
tice. 

10. Stimuli of low intensity placed on the forearm, are 

judged lighter than when placed on the palm of 
the hand or the index finger. 

11. The pain threshold for pressure varies with the place 

of stimulation, being greatest where the skin is 
thick and separated from the bone by muscular 
tissues. The temporal region of the head is the 
most sensitive, and the palm of the hand, the 
thigh, and the heel, are among the least sensitive 
parts. 



86 SENSA TIONS FROM PRESSURE AND IMPACT. 

12. Weights of .01 g. are about as easily perceived when 

impact is not entirely excluded, as weights of .4 g. 
when pressure only is applied, the time of appli- 
cation being 1-2 sec. 

13. The pain threshold for impact stimuli is determined 

by the product of the mass and the square of the 
velocity. 

14. In judgments of the intensity of impact stimuli the 

mass has in general more effect than the square of 
the velocity, but less than the velocity. 

15. Differences in velocity are perceived, on the whole, 

more accurately than differences in mass, but 
much less accurately than differences in the 
square of velocity. Individuals differ greatly, 
however. 

16. The discrimination for moving weights is about the 

same as for weights applied without appreciable 
impact. 

17. The area of stimulation does not, on the whole, affect 

the accuracy of discrimination for weights. But 
individual peculiarities appear in the results 
obtained. 

18. Pressure stimuli of small area are generally overes- 

timated. The extent of overestimation of inten- 
sity for an area -g- 1 ^ of 8 cm. was on the average \. 

19. The probability that a stimulus of very low intensity 

will be perceived is inversely related to the area 
of stimulation. 

20. The pain threshold increases with the area of stimu- 

lation in approximately a logarithmic proportion, 

21. The discrimination of areas is much better for stimuli 

of 200 g. than for stimuli of 800 g. 

22. The relative accuracy of discrimination for areas is 

not constant, but is greater for large areas. 

23. The probability that pressure stimuli of very low 

intensity will be perceived increases with the rate 
of increase of the stimulus. 

24. The relation between the time and intensity threshold 

of pain is approximately expressed by an hyper- 



SUMMARY. 87 

bolic curve. The appearance of pain as the time 
of stimulation is increased, is generally very 
gradual and difficult to determine. There is an 
intensive limit below which stimuli never cause 
pain. 

B. — Theoretical. 

1. There is no basis for the alleged identity of haptic 

and temperature sensations. 

2. Pain, tickle and pressure sensations are heterogeneous 

sensations induced by quantitative changes in the 
intensity of the stimulus. Dermal pain itself is 
probably a sensation and not merely an intensive 
form of the algedonic tone. 

3. Touch and pressure sensations are qualitatively the 

same. The apparent difference between them is 
really one of perceptive processes. 

4. The so-called threshold is not a true quantity. This 

may be shown by the same arguments that are 
applied to the so-called least noticeable difference. 

5. If the estimate of the intensity of the stimulus may be 

considered as indicative of a corresponding in- 
crease in the intensity of sensation, this quantity 
increases much more slowly than the stimulus. 
The apparent rapid increase for very high inten- 
sities may be due to perceptive processes and not 
be a true increase in sensation. 

6. The variation of the probable and constant errors 

renders inexact the use of the probability integral 
in the method of right and wrong cases. 

7. The variations in the confidence of observers and in 

the percentage of right cases in guessing, goes to 
prove that there is no such quantity as a least 
noticeable difference. 

8. The accuracy of discrimination is in general probably 

independent of the place of stimulation, except 
for very low intensities, which have less intensive 
effect at some places than at others. Practice 
seems to aid the discrimination at places not 
accustomed to pressure stimuli. 



88 SENSA TIONS FROM PRESSURE AND IMPACT. 

9. The intensive effect of impact stimuli for pain is 
equally dependent upon the mass and the square 
of the velocity. The intensive effect for such 
stimuli causing only impact sensations apparently 
increases faster for the velocity than the mass, 
but more slowly for the square of velocity than 
for the mass. If this be true, the stimulus for 
impact sensations is different from that for pain 
sensations, the stimulus for pain being mv 2 and 
that for impact sensations being mv k , in which k 
is somewhat greater than unity, and possibly sub- 
ject to individual variations. 

10. The intensity of dermal sensations, is inversely re- 

lated to the area of stimulation. If we assume 
any of the psycho-physical laws deduced, the 
intensity of the sensation increases much more 
slowly than the reciprocal of the logarithm of 
the area. 

11. The intensive effect of the area may be explained by 

the probable physiological process of stimulation, 
the effect upon the sensory nerves being dependent 
upon the energy expended upon the surrounding 
tissues. The stimulus in pressure sensations is 
not to be considered the force applied, but the 
work done by this force, or more strictly the 
energy lost by the mass applied. 

12. The intensity of pressure sensations decreases for low 

intensities with the time of pressure. For high 
intensities causing pain, the intensity of the sen- 
sation of pain increases with the time of pressure. 
The relation of the intensive effects of the time 
and that of the intensity of stimulation for pain 
sensations is probably that of a direct proportion. 

13. The time phenomena of dermal stimulation support 

the theory advanced as to the process of stimula- 
tion. They also tend to show that dermal pain 
is a distinct sensation. 



VITA. 

I was born in St. Louis, Missouri, July 4th, 1869. I 
entered the University of New York in 1886, having been 
prepared for college principally by private study. In 1887 
I entered the Sophomore Class of the School of Arts, Col- 
umbia College, and graduated in 1890. Since that time I 
have pursued post-graduate studies under the University 
Faculties of Philosophy and Pure Science ; in Psychology, 
with Prof. Cattell ; in the History of Philosophy, with 
Prof. Butler, Dr. Hyslop, and Prof. Peck (Roman Philoso- 
phy) ; in Biology, with Prof. Osborn, Prof. Wilson, and Dr. 
Lee; in Physics, with Prof. Rood and Prof. Pupin. 

HONORS AND DEGREES CONFERRED UPON THE WRITER. 

Scholarship in Latin, 1888. 
<< Greek, 1888. 
" " Greek, 1889. 

Degree of Bachelor of Arts, with Honors in Philosophy, 
Classics and English, 1890. 

Prize Fellowship in Letters, 1890-91. 
University Fellowship in Philosophy, 1891-93. 

PREVIOUS PUBLICATION. 

J. H. Lambert: " A Study in the Development of the 
Critical Philosophy," The Philosophical Review, January, 
1893. 



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